Zigzag exchange will cease operations in 2024 as server costs have exceeded the revenues from Bitcoin to Lightning exchanges. Over five years, we haven't lost a single payment, though there have been some incomplete exchanges.
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For LN to BTC exchanges or vice versa, use centralized exchanges like Bitfinex or Binance.
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Besides that, Mt Pelerin deserves to be mentioned as non-KYC instant/swap exchange IMO. In the same way as Bity they offer fiat exchanges without KYC (under $1000) thanks to the Swiss laws. They don't offer many different cryptocurrencies and mostly stable coins but they support LN transactions and their exchange rates are rather good unlike some other swap services.