How can I free a sticking valve in my 2003 Grand Marquis .?

FIRST of all WHAT OIL Are you using! HOPEFULLY NOT VALVOLILNE or CHEAP bargain OOIL CHANGES! Try using PENNZOIL ULTRA PLATINUM! It wil CLEAN as you DRIVE and give you extended warraty to 500,000 MIELS! IT is MADE from NATURAL GAS and NOT CRUDE OIL! IT MAY be a STUCK LIFTER! WHAT people just do NOT get, is that CHEAP WAXX based oils leave behind TAR< WAX< VARNISH and sometimes COKE! The LIFTERS are SMALL< like a BULLET! WHEN BAD OIL Is used, the oil will get STUCK inside the lifter and CLOG UP the oil passageways inside them! and then TICK TICK TICK!  The LIFETER will simply NOT expand anymore and the OIL will NOT stay inside it! if you can find an AMSOIL DEALERSHIP< get a can of AMSOIL POWER FAOM! ADD HALF to the ENGINE CRANKCASE< and use the OTHER half to clean the THROTTLE BODY and the IDLE AIR CONTROL VALVE! ALSO use DENSO TWIN TIP IRIDIUM LASER Spark plugs! POWER WASH the ENGEIN BAY with GUNK at a DIY car wash to remove years of JUNK around in near the RADIATOR!  THINK YOU  ONLY HAVE a sticking VALVE LIFTER! and AMSOIL combined with the PENNZOIL will free things UP NICELY and CHEAPLY! CHANGE the PENNZOIL ULTRA PLATINUM OIL every SIX months to a YEAR!  :EARN how to READ the OIL color and THINNESS! THEN change it! ONCE PENNZOIL gets to work it will SAVE ENGINE SENSORS and LAST LONGER between changes! The IRIDIUM :PLUGS will improve

EVERY ASPECT! MORE POWER< MORE ECONOMY and LOWER EMISSIONS all at ONCE! KEEP the ENGINE BAY CLEAN as SHOWROOM at all times! PENNZOIL will do the REST in time! REALLY! 

If it truly is sticking(engine lites  can't tell always exact problem), try SeaFoam or remove rocker arm/follower/cam;  tap on it with plastic hammer. Try to rotate it, too. If it Was stuck, you  may need a new valve guide.

I have seen engine lites come on, bad mileage, car running rich, trouble  was Bent Pushrods.  ECM over compensated by leaving injectors on  longer giving the rich indication., 

Take off and put back on the GAS CAP.  Usually the reason the engine light comes on.  It is weird, but a cheap fix if it works for you.  It will go off immediately.   Done; you fixed your car.  Now pay yourself $50.

I doubt you have a "sticking valve" if the only thing telling you that is a check engine light.

Do a compression check. THAT will tell you if a valve is stuck.

Do not assume.  Read the trouble codes first if you have not.  Test the injector if there is a misfire.  Get a compression and leak down test done and CONFIRM the bad valve.  If the valve is sticking, time for a top end rebuild or just get an engine from a junkyard.

Try using SeaFoam Spray that you can buy at any auto parts store. For getting intake valves cleaned up and seating correctly, treat the upper engine with Sea Foam Spray through the intake throat. You can also spray it through a vacuum line you have disconnected. Do this: Run the engine for 5 minutes, then shut off and remove the air cleaner… Then start the engine in neutral, have a helper hold the throttle steady while you spray bursts of SeaFoam Spray into the intake (there’s a red straw that comes with the can – cut to 7 inches or so and insert into the throat opening). Avoid spraying on the MAF sensor. With the throttle held 1,500 RPM over idle, spray in long bursts until half the can is empty, then shut off. Let engine cool and remove plugs to let sit overnight to soak. When ready to run again, replace plugs, start and let run for 5 minutes, then take a short ride to burn off the dissolved upper engine residue. Also add a can of SeaFoam Motor Treatment to the crankcase oil. This will help a sticking hydraulic valve lifter. Hopefully this will help. If not try it again. 

try using magnets or a trichotometric indicator support