OK, #[7] helped me solve it on Discord.
What I didn’t know is that you have to keep the browser window open after the swap or doesn’t send the transaction to your wallet. It just sat there waiting for me to go back to the page again. 
Discussion
Yeah gets killed by OS when in background. Still figuring out how we can improve UX here. Btw it's actually your browser *claiming* the locked coins.
Adding a step by step checklist on screen (perhaps even as a pop up) would do the trick, so the user could follow along during the process.
- Transaction received
- Swapping
- L-BTC / LN-BTC sent to wallet
- Received
- Swap complete!
Something along those lines…