Shutting down or closing Electrum while forward swap is ongoing will be an issue since your Electrum client acts as your lightning node.
-snip-
One more question, just to make sure that I'm understanding things correctly. I assume that this would also happen if I should do a Reverse swap. But would it also be the case outside of swaps, say if the party I'm sending an LN payment to is offline, or if I shut down after sending an LN payment but before they receive it (for whatever reason)?
It depends on the timing.
Because in 'Reverse swap', you'll just have to successfully send your lightning part of the swap to Boltz (
+fee that they'll use) and then an on-chain transaction broadcasted.
Since your part of the swap are all through lightning, it will take only a couple of seconds;
once the on-chain transaction was broadcasted, you can safely close electrum while it's waiting to be mined.
So in Reverse Swap, you only needs to wait for the on-chain transaction to be broadcasted (
status unconfirmed).
At that point, it's okay to close Electrum unlike in Forward Swap where you'll have to wait for your outbound transaction to confirm before Boltz initiate to send your lightning funds.