A technical question:
Is it possible to receive a BTC amount on-chain from another person and simultaneously open a LN channel for him/her with the same transaction, if the sender cooperates? Or even better: use a BTC amount on-chain transaction and refund an already opened channel (this would be a kind of splice-in)?
The on chain transition to you would need to have two (or more) outputs, 1 the 'on chain' transaction to you and 2 an output that gets 'locked' in a newly opened channel. This would work very similar to someone opening a channel valued less than the value of an input (less tx fees), and the remaining value being sent to one or more change addresses.