Do need a bank card to reserve with lyft or would a debit card work?

Credit or debit works fine for the deposit and you can use a different card for getting paid, that's what I did

Your pay will go directly into your checking account if that is the only card you use. I leased the car with a credit card though.

Debit or credit card will work just fine.

YES, after that you can tie that debit card for future use. But they need the deposit on a card attached to a checking account