The final table based on all of his predictions is at the bottom of this page.
In Lawro's league table, Chelsea and Liverpool finished joint champions and, overall, he has seven teams out of 20 in their correct positions going into the final round of fixtures.
Lawro has been pitting his wits against a different guest each week this season and his opponent for the final round of fixtures is drummer Ben Thatcher from rock band Royal Blood.
Thatcher is a Brighton fan who is looking forward to seeing his side in the top flight next season after their promotion from the Championship.
"If you look at where the club was 20 years ago, getting to the Premier League is an amazing achievement," he told BBC Sport. "It is going to be a great season.
"It will be all about staying up and, with the right signings, it can happen. We might even do a Leicester and win the title - who knows?"
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The Seagulls held their promotion parade last week after returning to the top flight for the first time since 1983.
"It was a day that the club will always remember," Thatcher said.
"I won't remember it as well as most people because I got off a plane and went straight down to the seafront and partied hard.
"But it was great to see how excited the whole city was that we had been promoted - it has pulled everyone together and we are all supporting our club."
A correct result (picking a win, draw or defeat) is worth 10 points. The exact score earns 40 points.
You can make your Premier League predictions now and compare them with those of Lawro and other fans by playing the BBC Sport Predictor game.
All kick-offs 15:00 BST
Arsenal v Everton
It appears Arsenal manager Arsene Wenger is going to stay on for another year or two and, if that is the case, I am not sure why they have kept it such a big secret.
So, it does not look like this will be Wenger's final game at the Emirates Stadium, but it could be Alexis Sanchez's - the future of the Gunners striker is still in doubt.
Arsenal have got next week's FA Cup final to think about but I don't think that will affect the result, because they can still finish in the top four and they have to go for the win in case Manchester City or Liverpool slip up.
Everton will finish seventh whatever happens and they will make a game of it, but the Gunners are on a good run and I think they will come out on top.
However, even if Arsenal do win, I think it will be too little, too late for Wenger's side as far as making the Champions League places goes - I think Liverpool and City will both win.
Lawro's prediction: 2-0
Royal Blood's prediction: This is going to be a great game - Alexis Sanchez is going to put Arsenal ahead and Everton will bring it back in the 70th minute. 1-1
Burnley v West Ham
Other than their win over Tottenham, West Ham's season has tailed off in the last few weeks.
Yes, the Hammers are missing some injured players but they have been very average for a while.
When their fans look at this season, it is their new stadium and their summer recruitment that have been the bugbears for them.
For a while it looked like Slaven Bilic's side were going to get dragged into a relegation skirmish but they are going to get a mid-table finish, which is probably what they deserve.
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West Ham are not a bad side when everyone is fit but, if they want a repeat of their seventh-place finish in 2015-16, they definitely need to sign some better players.
Burnley's target this season was to stay up and they have done it. It is mission accomplished and they can build again, which is great.
Their home form has been the key and I think it helped that they got an 'extra' match at Turf Moor early in the season - the venue of their game with Liverpool in August was switched because Anfield was not ready.
They won that game which not only gave them points on the board but it also set the tone for the rest of the campaign. They have never really been under much pressure.
Lawro's prediction: 2-0
Royal Blood's prediction: 1-2
Chelsea v Sunderland
Chelsea will get their hands on the Premier League trophy at the final whistle and and will want to sign off with a win but I am not sure what sort of team Antonio Conte will pick before the FA Cup final.
He made lots of changes for Monday's win over Watford but will have to be careful about doing the same for this game.
If, say, striker Diego Costa does not play then he will go two weeks without playing before facing Arsenal at Wembley and it is easy for players to lose their edge.
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Whatever team Conte picks, I don't think Sunderland will be able to stop the Blues from finishing their title-winning campaign on a high note.
There are more questions than answers about what will happen next at the Black Cats, and the only thing we really know is that they will be in the Championship next season.
Lawro's prediction: 3-0
Royal Blood's prediction: This is top versus bottom but I wonder who will play for Chelsea? I hope they give some young players a chance, and I think they will win anyway. 3-0
Hull City v Tottenham
Hull were relegated after losing to Crystal Palace last week but it was their home defeat against Sunderland in their previous game that really did the damage.
Tottenham said goodbye to White Hart Lane with a deserved win over Manchester United and they will want to finish the season strongly despite missing out on the title.
People will say they did not win anything but Spurs are a very good side who came close to winning the title - they did not bottle it one bit.
Spurs manager Mauricio Pochettino is doing a great job and the rest of the top six would take a lot of their players if they could - that is how good they are.
Analysis: I'd back Spurs for the title if they were staying at White Hart Lane - Jenas
Lawro's prediction: 0-2
Royal Blood's prediction: 0-2
Leicester v Bournemouth
Bournemouth have already bettered their points tally from last season, despite having a slippery month or two at the start of 2017.
Joshua King has been brilliant since Callum Wilson was injured at the start of February and the Norwegian striker has made astonishing progress as a player since I saw him when he came on loan to Preston in 2010.
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The Cherries are already in the top 10 and, if they can become a little bit meaner defensively, then they can continue their progress next season.
Leicester will go above them - and into the top half - with a win, however, and that is what I think will happen.
I do not understand why the Foxes have not revealed yet whether Craig Shakespeare will stay on as manager, but he deserves to keep the job because he turned their season around.
Lawro's prediction: 2-0
Royal Blood's prediction: 2-2
Liverpool v Middlesbrough
A win for Liverpool will secure a top-four finish and surely even they cannot slip up this time.
It is all very well saying because Middlesbrough are down already, the pressure is off them and they can go to Anfield and play their football - well, I have not seen Boro play any for the past 37 games.
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One big effort from Liverpool will get them over the line, and there will be a good atmosphere which will help.
It is a big game and if they are not revved up and they cannot beat Boro, then they do not deserve to be in the Champions League.
Lawro's prediction: 2-0
Royal Blood's prediction: 3-1
Man Utd v Crystal Palace
Crystal Palace are safe from relegation and in normal circumstances I would be expecting an open game on the final day of the season.
But I have no idea what sort of team either manager will put out, so it is very difficult to predict the outcome.
Jose Mourinho will make lots of changes before Wednesday's Europa League final, but he has such a big squad that it could still be a strong Manchester United side, if he wants it to be.
Lawro's prediction: 1-1
Royal Blood's prediction: United have not had a great season and might rest a few but I think they are going to win this one. 2-1
Southampton v Stoke
Southampton are guaranteed a top-half finish and can make sure of a top-eight finish with a win, which underlines that they have had another very good season.
Stoke's form has been heading in a downhill direction for a while now but the nature of the last day of the season always throws up some unexpected results, and I think this game will provide one of them.
Lawro's prediction: 1-2
Royal Blood's prediction: 2-0
Swansea v West Brom
This could have been a very tense affair but the pressure is off Swansea after they secured their survival last weekend, and instead it will be party time for them.
I was at West Brom's defeat at Manchester City on Tuesday and they will not change - Tony Pulis will set them up to try to make life difficult for the opposition.
Again, this game is hard to predict because there is nothing really riding on it but I think Paul Clement will have three points to celebrate, as well as staying up.
Lawro's prediction: 2-1
Royal Blood's prediction: 1-1
Watford v Man City
I had been wondering for a while what was going to happen to Watford boss Walter Mazzarri, and it was no surprise when it was announced this week that he will be leaving.
I think the Hornets will play well in his farewell game but I still think Manchester City will get the win they need to secure third place.
City are playing well and I thought Vincent Kompany looked great at the back when I watched him against West Brom at the Etihad Stadium on Tuesday.
An open game would definitely suit Pep Guardiola's side and surely Watford will not sit in, because what would be the point of that?
Lawro's prediction: 0-3
Royal Blood's prediction: City are going to destroy them. 1-4
Lawro was speaking to BBC Sport's Chris Bevan.
Lawro's best score: 140 points (week 22 v James McAvoy)
Lawro's worst score: 30 points (week four v Dave Bautista)
From last weekend's Premier League matches, Lawro got six correct results, including two perfect scores, from 10 matches, for a total of 120 points.
He beat world tennis number one Andy Murray, who also got six correct results but with one perfect scores for a tally of 90 points.
Lawro also picked up 40 more points for correctly predicting the outcome of the four midweek fixtures, with more to come depending on Leicester v Tottenham on Thursday.
BBC Sport's football expert Mark Lawrenson has made a prediction for all 380 Premier League games this season.