Is the battery brand new? Like, was it previously showing the BAT indicator and you just installed a new battery? If that's the case, that BAT will stay there until it does another battery check. Could be a few hours, could be a day. You might be able to manually trigger a battery test by entering your code then 5/test. That works on Vista panels, but I'm not sure about the Lynx.
Is it showing BAT by itself, or with any other numbers? If it says "BAT 02", that's a transmitter battery.
There isn't a real accurate way to test those battery packs. You could unplug the lynx transformer and see if the backup battery powers the system. If it powers down right away, then the battery pack is bad.