Shutting down or closing Electrum while forward swap is ongoing will be an issue since your Electrum client acts as your lightning node.
Electrum's lightning feature isn't custodial so it needs to be active to be able to receive lightning funds.
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)?
Btw. no problems with forward swaps anymore!