We've received a couple of similar support cases over the past few days. We can confirm that there is an issue for the moment running the .dmg LsAgent installer on Mac OS Monterey, be it on an Intel or an M1 chipset.
We've escalated this to our developers so they can investigate further. Once a root cause is determined a fix will be added in a future release. When a fix for this issue is added it will be referenced as LAN-11502 on the page below.
https://www.lansweeper.com/changelog/
As a temporary workaround, you can mount the LsAgent installer using hdiutil and install by doing the following:
In Finder, go to Applications -> Utilities -> Terminal
Go to the download pad of the LsAgent dmg file
Mount that file using hdiutil attach LsAgent-osx_8.4.100.43.dmg
After mounting the file, you should have the mounted image in Finder from where you can start the installer: