If Adobe discontinued Lightroom, your existing catalogs would not suddenly become useless. In general, installed software can keep working without ongoing support, especially with perpetual licenses; with subscription software, access may become limited, but catalog data would still exist.

Lightroom catalogs are stored in a fairly accessible database format, so metadata such as organization, keywords, and other catalog information would likely be recoverable if needed. If Lightroom were ever abandoned, it’s reasonable to expect third-party migration tools or importers to appear, much like happened for Apple Aperture.

The main limitation is edits: Lightroom’s non-destructive develop adjustments are not guaranteed to transfer cleanly into other software. In practice, metadata may migrate, but image rendering/edit history often will not. To preserve the visual result of edits, exported files such as TIFFs would be the safest option.

So the short answer is: catalogs would likely remain accessible, metadata could probably be migrated, but full edit compatibility with other software is not something you should assume.