No. Skylum builds Luminar for Windows 10 and newer and for macOS only. There is no Linux version and no browser version, so a switcher needs a different editor.
Luminar Neo by Skylum · Photos & graphics · No way to run it
Skylum's own system requirements page lists Windows 10 version 1909 or higher, 64-bit only, and
macOS 12 or higher. Linux does not appear, there is no web edition, and buying a licence does not
give you access to anything that runs on Linux.
Luminar's appeal is that it does heavy edits with one slider. Sky replacement, relighting, skin
smoothing and its portrait tools are mostly one click, and that is the part that is hardest to
reproduce for free. GIMP and darktable will get you to the same place but with more steps and more
judgement from you.
darktable is the closest free starting point. It develops raw files, corrects exposure and colour,
and keeps your originals untouched. GIMP takes over for the retouching, including removing
distractions and working on a portrait in layers.
Your photos travel fine. Luminar keeps its edits in its own catalogue, and no Linux program reads
it, so export anything you have finished as a JPEG or TIFF before the Windows machine goes away.
Another free raw developer, with more detailed control and a steeper start.
Your files: Opens the same raw, JPEG and TIFF files.
This doesn't have to stop you
One stubborn program doesn't have to decide the whole question. You can keep Windows on the same PC and restart into it only when you need Luminar Neo. Everything else you do can move.