IIRC, a deposit is made by two parties to create a lightning network channel that's enough to cover all transactions (kinda like a multi-sig escrow), and both parties have to sign-off on their balances after every transaction (the last balance signed by both parties is the only valid state). I think most people would use a custodial wallet where the custodian already has channels set up, and this would require trust in the custodian. Lightning networks didn't exist, and wasn't fully spec'd out the last time I looked into it though.