At least directly with lightning, it’s not immediately obvious how you could reveal a key that only allowed you to spend up to some limit. The normal setup in lightning is your key can sign for the whole 2-of-2 channel balance. With pre-setup you could have some extra output on the commitment transaction and a new sub-channel that you could give the recipient control over, but you’d need to have that set up in advance for the exact amount you want to send (and it’d be a fairly complicated protocol extension for everyone to support). Probably just use ecash for the initial minute and then pay with lightning for further minutes after you’re online.