How does a Lightning transaction work if one party starts with no Bitcoin and no wallet?
The classic example assumes that Bob is locking some Bitcoin of his own on the blockchain, and Alice and Bob are both funding a channel between each other.


This is not how lightning currently works! Currently only one side is funding the channel. People are working for a dual funding solution in which two parties fund the channel in a way how you suggested it. So if Bob does not have any Bitcoin alice could fund the channel and then send btc to Bob. (which should also be the answer to your question)