As long as the appropriate commands are installed, agentless scanning should still work the same as any other Unix or Linux system. The installation would be the same setup of SSH and sudoers. The exact steps may be different (for example if you're not using OpenSSH) but as long as Lansweeper can connect and run the commands it should be the same from there.
LsAgent should work, but if it can't find a certain library or the right version it may have trouble. This can happen with some distributions that update or drop support for certain versions of libcrypto/libssl for example. I'm not aware what libraries Solaris ships with so not sure if that would come into play.
I'd encourage you to try it and see if it works. I may be able to spin up an OpenIndiana VM and do some testing. Of course, our technical support staff will also be happy to help if anything doesn't work: