Being closely integrated with the rest of the system & libraries is a feature, not a bug - no plans to change anything about it :^)
That being said, it's definitely possible to use it outside of SerenityOS as a regular library, just need a checkout of the serenity source for that.
See https://github.com/linusg/libjs-test262 for an example, specifically the CMake files and `src/main.cpp`.
The separate website is just to have a nice & short link to the test262 graph and whatever else we'll put there eventually; and also because it's built/deployed in a slightly different way than the main serenityos.org website.
Lagom covers many libraries, including various ones used in the Browser/LibWeb (e.g. LibJS, LibWasm), but LibWeb itself is not part of Lagom and doesn't currently build or run on Linux. It's absolutely possible, but no one is working towards it specifically at the moment.
There's a list of things needed to make that happen here: https://github.com/SerenityOS/serenity/issues/10968