My 2008 f-250 looses the low beam on passenger side on both the chassis and the plow lamps. when the western plow lights are plugged in.

Look for a bad or broken ground wire on that circuit.

there are 2 lamps. both dead, (shoe drops)......
low beam dead on both sides?

most cars have 2 fuses. so if one side shorts, your not blinded.
check fuses first.
if fuses measure 0 ohms, they are good. (DMM , low ohms range)

if problem is more complex. then that.
we can find it in 5min with any voltmeter ever made. 1920 to now.
got a meter? (walfart has em,)

Check for loose contacts in the light socket. Also, most vehicles use separate relays for passenger and driver side headlights, so be sure to check those.

checa la palanca de cambios de luces

You have lost the ground, evidently on the left side. The lamps act that way because one of the lamps is grounding through the elements of the other lamp.

in low beams or high or both?
that is caused by:
1: bad held lamp. old lamps can go dim.
swap left and right, if dim follows bulb, bingo weak bulb or wrong type bulb. buy matching blubs (same brand and P/n)
2: bad wiring to lamp. damaged wires, or connectors to same.
4: bad combo switch. (if low beams)
5: bad fuse or holder, corrosion , to either.
head lamp fuses. there are 2. left and right.
6: hackers, many hackers put in wrong lights. inspect it.

It can be faulty low beam lamp or its connection issue for low beam lamps.

There are few solved helps links with proper solution to troubleshoot these issues.I suggest you to refer the links below.Click the link:----
Passenger side low beam out?

http://repairhelpcenter.blogspot.com/2012/01/passenger-side-low-beam-out.html

------------
Low beam HID light goes out? http://schematicsdiagram.blogspot.com/2012/01/low-beam-hid-light-goes-out.html
----------2007 Dodge Caliber: Low Beam Headlight Not working http://technoanswers.blogspot.in/2012/06/2007-dodge-caliber-low-beam-headlight.html
-------------Chevy Tahoe: Low Beam Lamps are not working? http://technoanswers.blogspot.in/2012/04/chevy-tahoe-low-beam-lamps-are-not.html
----------2001 Chevrolet Tahoe: Both Low Beam Lamps Not Working? http://technoanswers.blogspot.in/2012/04/2001-chevrolet-tahoe-both-low-beam.html
--------------2002 Toyota Tacoma: Low Beams not working? http://technoanswers.blogspot.in/2012/04/2002-toyota-tacoma-low-beams-not.html
-----------Low beam headlights Modification? http://schematicsdiagram.blogspot.in/2012/04/low-beam-headlights-modification.html
-----------DRL and Low beams not working? http://schematicsdiagram.blogspot.in/2012/04/drl-and-low-beams-not-working.html
-----------These will help.Thanks.

get a test light and check plug (connector) to headlamp. one hi beam , one low beam and ground. if they light , lamp is bad, if the test light is confusing just switch headlamps from side to side and see if the lamp that does work works on other side or plug.

check the bulbs first and also the fuses theres a fuse for each side and for low and high beams, start there, good luck.

Headlights in my '03 Jeep Cherokee are through a relay, both both light's are on the same relay I believe.

I would be suspect of any added modules which drive the headlights. Hopefully, they didn't "splice" in, but used one with factory connectors, so you can remove the module and reconnect the connectors as the vehicle was shipped from the factory.

When it's all said and done, you really need a wiring diagram for the vehicle. I can get one for my Jeep at the local repository library. Don't know about your truck. You may be able to find a diagram through some hard searching on the www.

Let me know if you need someone to bounce thoughts off of.