If I hit a car in my driveway and just found out that my insurace has lapsed, what am I liable for?

If you were at fault  in hitting the car--that is, you were driving negligently (carelessly) or recklessly, such as by not looking where yo were going, driving too fast, driving distractedly (e.g. on phone or texting), DUI, etc.--then you are potentially liable for all costs and damages which you caused. These include the cost to repair the other car, if repairable, or its then-current value if it can't be repaired; any medical costs or lost wages incurred by an injured person; possibly pain and suffering for serious injuries; and other out-of-pocket costs, like if someone else had to rent a car while his/her car is in the shop.

If someone else carelessly caused damage to you, on the other hand, they would potentially be liable for your costs and injuries.

An at-fault person, whether you or another driver, will have to bear his/her own costs (includinig repairs, medical bills, etc.), unless and only to the extent they have applicable insurance to cover those costs.

If you only you were involved--i.e. you were driving one of your cars, and hit another of your cars--then again, you'd have to bear all costs unless you have appropriate insurance.