To accept cryptocurrencies, enable one or more of the following alternative payment methods from the Payment providers page of your Shopify admin:
  • Coinbase Commerce
  • BitPay
  • CoinPayments.net
Shopify Help Center > Alternative payments > Cryptocurrency https://help.shopify.com/en/manual/payments/alternative-payments/cryptocurrency
None of those support LN. Coinbase and BitPay are anti-bitcoin, and LN cuts into Coinbase's business model (where they would rather have you trade your BTC into shitcoins than to spend it) so don't expect LN support from them anytime soon.
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