The home side were all out for 249, having been 195-6 overnight, when Jarvis had Charlie Shreck lbw with the first ball after a long hold-up.
Lancashire began their second innings 119 in front, but needing to press on to have a chance of a positive result.
They lost Paul Horton and Karl Brown in reaching stumps on 39-2, a lead of 158.
With so much time lost to the weather, a draw appears the only realistic result unless Lancashire collapse spectacularly on the final morning or skittle Leicestershire after setting them a target.
Having begun play at 12:15 BST, only 13 overs were possible before the players were forced from the field again until 17:30 BST.
Tom Wells was lbw to Jarvis in the first phase of play, but the key wicket of Mark Cosgrove for 79 went to former Leicestershire seamer Nathan Buck, who took 3-64.
Leicestershire seamer Clint McKay:
"The game is moving on quickly and you never know what's going to happen.
"If we can bowl as well as we did last thing, and pick up two or three early wickets, suddenly it's a very different game."
Lancashire director of cricket Ashley Giles:
"There is still a lot to be done, and the first priority for us is to get a few more runs on the board and get a good lead.
"We've not set any targets but there is enough in the pitch for wickets to fall pretty quickly and in clumps.
"I just hope it's a clear day and it could be a fun day, all three results are possible."
Pace bowler Kyle Jarvis claimed 5-69 for Lancashire as they earned a sizeable first-innings lead on a rain-shortened day against Leicestershire.