I wouldn't say benching "works" the lower back in any major sense. If you're in a good position and keep everything tight, then sure you'll feel everything contract, from traps to low back to glutes and hams. And if your low back isn't well-conditioned, it would make sense that it gets "tired" from benching. The amount of arch you do or don't use will also be a factor. More arch, more low back "work".
But all in all, I'd say the bench press works the lower back about as much as squatting "works" the biceps. There's tension in the muscle during the lift, but it's from providing stability, not from actually helping to move the weight.