No. Streamlabs Desktop is built for Windows and Mac only. OBS Studio, which Streamlabs was built on top of, has an official Linux version and does the same streaming and recording job.
Streamlabs Desktop by Streamlabs · Video · No way to run it
Streamlabs lists Windows and macOS in its system requirements and nothing else. There is no Linux download and no
browser version that replaces the desktop program.
OBS Studio is the answer, and it is a closer landing than it sounds, because Streamlabs Desktop was built on OBS in
the first place. Scenes, sources, filters and the streaming settings all work the same way. It is free and installs
from your Linux system's app store.
What you give up is the Streamlabs layer on top. The built-in alert boxes, the themes, the tip page and the chat
widget are not part of OBS. Streamlabs alerts and widgets are web pages though, so you can add them in OBS as a
browser source and keep your existing Streamlabs account and alerts working.
Your channel, your followers and your Streamlabs account are untouched by any of this. If you pay for Streamlabs
Ultra, check what you are still using before you renew, since the desktop program is no longer part of it.
The program Streamlabs Desktop was based on, with an official Linux version. Scenes and sources work the same way. Alerts and themes come back by adding your Streamlabs widget pages as browser sources.
Your files: Cannot import a Streamlabs scene collection directly. Recordings are ordinary MP4 and MKV 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 Streamlabs Desktop. Everything else you do can move.