Is it possible to create a binding contract verbally to share lottery winnings?

Yes, but some contracts are required to be in writing, so you have to be careful not to fall in one of those categories.  Also, contracts generally require consideration (quid pro quo) to be valid.  For example, contracts which can't be performed within a year generally have to be in writing to be enforceable, which means that an agreement that you will, out of the goodness or your heart, share any lottery winnings you have in 2016 would have to be in writing to be enforceable and also would be invalid for lack of consideration, while an oral agreement to share any 2014 lottery winnings in exchange for the other party agreeing to clean your house once a week for the next 3 months, probably would be enforceable.