Welcome to Pet Talk. You'll find a lot of help here.

I'm just now getting Sidney to be a lap kitty, and he's six years old! (well, his definition of a lap kitty is that I can get him to stay on my lap for one to two minutes)

You might want to try setting her next to you, instead of on your lap. I did this with Sidney, and he seemed more accepting of it. Other than that, I think you just have to give it time and patience. There are wonderful stories here on PetTalk about a cat named Fister. It took his humans a long time to make him more tame.

Good luck!