Lollipop killed my nexus 7 too. I was going to give up and throw it in the garbage and decided to do a factory reset on it. Now it is marginally usuable, I don't feel like throwing it at a wall or smashing it under my boots any more. But it still sucks pretty bad. It worked the best with 4.1 on it. Every upgrade has brought worse performance to it.
Try a factory reset.