A common problem with 2002 LS's are the DCCV, (Dual Climate Control Valve). Pretty expensive, so I suggest finding someone who know's how to reset the climate control and see if that helps. Other than that, you might need to check the DCCV. Also, a no-brainer, make sure your R-134a is topped off. Hope this helps.
Have Auto Parts Store reset it , will do this for free.
I have a 2002 Lincoln ls and mine is located in the d/s panel by your left foot. Pull the panel and its a red button
Where is camshaft sensor on 2002 Lincoln ls
Unplug battery for 30 minutes then plug back on that will reset the ecm
broken dccv... look for dual climate control valve in the answers...
What is the firing order of a v6 lincoln ls 2002?
where is the 5 coil located on a 2002 Lincoln ls
On a 2002 Lincoln LS : ( 68 litres / 18 U.S. gallons )
Change the filter and hit the reset button on the information center which is located above the radio. If the above fails take it to a dealer and have them reset it.
You can refer to your user manual to see the fuse diagram for a 2002 Lincoln LS.
The (DCCV) dual climate control valve may be damaged also called heater control valve.