Access to all data of users, games, puzzles and etc on Lichess.
Lichess API is a free Games & Comics API that requires OAuth authentication, is served over HTTPS and has unconfirmed CORS support.
Details from lichess.org.

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The Lichess API is provided by Lichess.org API Docs (lichess.org).
Yes. The Lichess API is listed in the Games & Comics category of the public-apis directory, which only includes APIs that are free or have a free tier. Check its documentation for rate limits and paid plans.
Yes. The Lichess API uses OAuth authentication, so you need to register for credentials before making requests.
CORS support for the Lichess API is unknown. Test a request from the browser, and fall back to a server-side call if it is blocked.
Yes. The Lichess API is served over HTTPS, so it's safe to use in production.