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There are a number of "swap" services that have support for Lightning Network. From the post from the following, look for entries with the "⚡", which indicates LN support.
So what you are doing is sending LN and receiving in bitcoin. Fees may vary significantly from one service to the next. FixedFloat is probably the most popular swap service, but it doesn't work when accessed from the U.S.
Instant Exchanges / Swap Services which do not require identity verification / KYC https://cointastical.github.io/KYC-Free-Instant-Exchanges/