Verdict: Partly
Partly. There is no Lightroom to install on Linux, but if you use the cloud version of Lightroom your whole library opens in a browser at lightroom.adobe.com with a paid subscription.
Adobe lists Lightroom for desktop, mobile and the web, and confirms the web version at lightroom.adobe.com. Linux appears nowhere. The older Lightroom Classic, the one that keeps photos in folders on your own drive, is Windows and Mac only and has no browser version at all.
So the answer depends on which Lightroom you use. If your photos already sync to Adobe's cloud, the browser version on Linux shows the same catalogue, the same edits and the same albums, and lets you keep editing. If you are a Lightroom Classic user with a local catalogue, there is no route that keeps working.
The practical replacement is darktable. It is free, works the same way Lightroom does by leaving your original files untouched and storing the edits separately, and it handles raw files from nearly every camera. It is less friendly than Lightroom and the sliders are arranged differently. digiKam is the better choice if what you mostly want is to sort, tag and find photos.
Your photos themselves are never at risk, because Lightroom only ever edits a description of the changes. What does not travel is the catalogue. darktable cannot read a Lightroom catalogue, so your edits start again. Before you leave Windows, export finished photos as JPEGs or TIFFs so you keep the versions you care about.
Free raw editor built on the same non-destructive idea as Lightroom. Capable, and genuinely harder to learn.
Your files: Opens your raw files and JPEGs directly. Cannot import Lightroom catalogues or edits, so exported versions are worth keeping.
Strongest for organising, tagging and searching a big photo collection, with editing attached rather than at the centre.
Your files: Reads raw files and existing tags written into the files themselves.
For heavier edits on single photos once darktable has done the developing.
Your files: Opens JPEG and TIFF exports. Raw files need a helper, which most Linux app stores install for you.
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