From my experience, Teams has to be installed in the User context, using the currently logged on user. It lives within the C:\Users\<username>\AppData area.
There is a way to "pre-deploy" Teams to each computer, then when a user logs in, Teams' own installer will install it within their profile. This is a Microsoft install technique, not a Lansweeper feature. I tried the MS trick on a few machines, and found it to be clunky. I have Teams installing/updating via login script and via Teams, but using the "Currently Logged On" Run Mode.