Through liberal use of the dictionary for Microsoft Lync, the Accessibility Inspector, and a few web links, I’ve come up with this script which toggles the mute button in Lync for Mac.

tell application "Microsoft Lync"
  activate
end tell
tell application "System Events"
  tell process "Microsoft Lync"
    repeat with aWindow in (get every window)
      set aName to get the name of aWindow
      set initialName to ((characters 1 through 12 of aName) as string)
      if (initialName = "Conversation") then
        activate aWindow
        click checkbox 5 of splitter group 1 of aWindow
      end if
    end repeat
  end tell
end tell

I still want to hook it up to a hotkey, and ideally, have a different hotkey for mute and unmute, but that will have to be left for another session. I will hopefully update this post with more details as I figure out how to explain them.