Training for sprints / short races
Anaerobic training is without oxygen, so you are using the lactic acid energy system. This means to be going above 80% of your Max Heart Rate MHR (or above 8 on perceived exertion table (can barely talk)). If you are solely in the anaerobic region, you can only go for 2 mins (ish) at that intensity. This means you will need to be in between regions, so you are using both major energy systems (with and without oxygen) to last 7-8 mins (of last lap).

If you are to use perceived exertion rather than heart rate you basically have to go hard out the whole time. You have said that you get gassed on the first lap i.e. perceived exertion is high, this could be due to an insufficient warm-up as Slovakok mentioned. This is where heart rate is helpful, it is accurate and tells you exactly what you are doing. Other wise, you could do one lap and get gassed then once you settle in start to go a bit harder to match the perceived exertion of the first lap.

A good way to get into the anaerobic zone is to do interval training, maybe once a week you could do three laps with a rest in between each lap, go as hard as you can for one lap, then rest until your heart rate feels normal again, or you think you can repeat the effort (might be 5-10 mins rest), then next lap go hard again, then rest a similar time... The next week try to rest for less time and continue decreasing rest until you can do 2 laps at that intensity or something like that. Other things to try are hill sprints, plyometrics, time trials, and just training in the anaerobic zone as much as possible, also training's work differently for different people, so you need to find something which works for you.

Basically you should set some goals for where you want to be in x weeks, and remember that  to be able to race at anaerobic level you must train there as well. So just go hard or go home on that final lap i guess (in both training and racing).