My house is over 100 years old and the stone basement walls are coated with lime. Can I paint over it? If so, with what products and what do I need to do to prep it.

I can't imagine you could paint over it with success.

Clean and dry is always the best. No product out there will work without proper surface preparation.

Call your local Sherwin Williams (commercial) service desk and talk with them. I find most of the time, they will know or can find out. Sherwin Williams has an entire industrial division that has paint and coatings for almost any surface.