If you find the quality on archive.org lacking or the legal gray area uncomfortable, consider these legitimate alternatives:
This is the most critical fact to understand. The Blue Lagoon (1980) is not in the public domain. It was produced by Columbia Pictures (now Sony Pictures Entertainment), and the copyright is actively enforced. The screenplay, the musical score by Basil Poledouris, and the film elements themselves remain under full copyright protection until at least 2050 (95 years after its release under current US copyright law). the blue lagoon 1980 internet archive
: It allows users to stream or download archived versions, such as the Columbia Pictures version. The Blue Lagoon (1980) - A Timeless Classic
So go ahead. Search the Archive. Watch Emmeline and Richard build their raft and discover the mango grove. But watch with critical eyes—understanding that paradise, on film and online, is always more complicated than it appears. The Blue Lagoon (1980) is not in the public domain