I personally like a bolt rifle for serious squirrel hunting, but there are some very good lever actions -- notably the Marlin 39A and the discontinued Winchester 9422.
My favorite squirrel rifle is a Kimber M82 bolt gun, with a Burris Mini 4X scope. I practice offhand at 50 feet on an 11-bull 50 foot NRA target. The idea is to empty the magazine (5 rounds) on each target, working the bolt from the shoulder. I hesitate to estimate how many rounds I've fired that way -- but many a 5,000 round case of .22s has gone up in smoke.
I also used to shoot this rifle in Smallbore Silhouette matches, where the ram, shot at 100 yards, is just about the size of a squirrel. And I have shot squirrels out to 100 yards with this rifle.