How sharp is the pain? If we are talking about a dull feeling of pressure in the lower lumbar pressure that is quite uncomfortable then we are probably talking about back pump. Any muscle can get a pump, and after 20 rep sets it's pretty much a given. However, if the pain is sharp, then we might be looking at a strain or tear.
Dealing with Back Pump
Back pump is just the same phenomenon as when your biceps get pumped after doing a lot of curls. The only difference is that the location of the pump is very uncomfortable. Just as 20 minutes away from the bar will clear up a bicep pump, the same is generally true for the back pump. The only difference is that the muscles are larger so it can take a little longer for that discomfort to dissipate.
Back pump is only uncomfortable, but it is associated with fatigue. Considering that 20 rep squats are very fatiguing to the body, you may want to focus on rep ranges between 6-12 and just do more sets.
Dealing with Back Strain
A strain in your muscle is a very sharp pain, that occurs whenever you cause damage to the muscle. Here's the important thing: a damaged muscle needs time to repair. That means you'll have to:
- Rest--compression, cold and hot compresses, etc will help the muscle relax
- Train around the injured muscle (i.e. don't do exercises that aggravate it, but try to find something that you can do)
- Start light to test the waters when you feel confident enough about resuming
Other things you can do
I do recommend working with someone who knows barbell movements to see if they can find anything wrong with your technique. We all have things we can work on. In my case, my coach diagnosed some anterior pelvic tilt and gave me some stretching exercises to help correct that problem. I was able to squat better after applying the advice. He also suggested some tweaks to my squat form that made it work with my leverages better.