I'd consider a "dry" lubricant.  It won't collect dirt, and cause problems
down the road.

The headlight pop-up mechanism has "direction" switches, and relays
associated with it.
To check if it's a "stuck" mechanism, have someone turn the lights off,
while you have your ear close to the pop-up lights.
If you here a motor sound, straining, then your mechanism needs cleaing and
lubbing.  However, since both lights have the same problem, it's unlikely
it's a "stuck" mechanism.

According to the wiring diagram, there is a relay (called a "Passing control
Relay") that is controlled by the pop-up light switch.
Applying power from the "pop-up switch" to pin 3 of this relay, causes pin 1
of this relay to become energized for a few seconds , which causes the
"pop-up" relay to energize and power the motor of the pop-up lights, to
raise the lights (if they are down).

Applying power from the "pop-up switch" to pin 5 of this relay, causes pin 2
of this relay to become energized for a few seconds, which causes the
"pop-up" relay to energize and power the motor of the pop-up lights, to
lower the lights (if they are up).

The motor direction, of operation, is determined by switches internal to
each motor assembly, independantly.

If both lights are doing the same thing, then I would suggest checking the
"passing control" relay.  It is an electronically (internal to the relay)
controlled  device.
Looking at the wiring diagram, and in your case, I would think that
reversing pins 1 and 2 would cause the opposite to happen with the lights
(they would only go down, but never come up).
If you have a voltmeter, check pins 1 (up enable) and pin 2 (down enable)
for 12 volts (for 5 seconds AFTER you operate the switch), when you operate
the pop-up switch.  These are the OUTPUT pins of the passing control relay.
Also check pin 5 (pop-down enable) and pin 3 (pop-up enable) for 12 volts
when you operate the pop-up switch, .  These are the passing control relay
INPUTs that tell the relay what to do on the output.
If pin 3 has 12 volts then pin 1 should have 12 volts for approximatly 5
SECONDS after pin 3 is energized.
If pin 5 has 12 volts then pin 2 should have 12 volts for approximatly 5
SECONDS after pin 5 is energized.

Relay connection, pin numbering
_____
/1|X|2\

--------
"X" has no pin.
I use my wifes sewing pins to piece the wire insulation so I can attach the
meter leads.  Just be careful you don't go to far and short the wire to
ground.

Also, try this at your own risk, This will test the motor drive circucts.
Test 1;
Make the lights pop-up.
Turn the ignition OFF.
Unplug the passing relay connector from the relay,
Turn the ignition key to the run postion.
Applying 12 volts (for about 5 seconds) to the pin 2 (blue wire with a red
strip) contact of the plug attached to the cable.
The lights should go down.
Applying 12 volts (for about 5 seconds) to the pin 1 (blue wire with a
yellow strip) contact of the plug attach to the cable.
The lights should go up.

If this test passes, your mechanical pop-up light system is working. Go to
test 2
If this test fails, check your wiring to the engine compartment, and retest
by applying 12 volts momnetarily to the same colour wires at the pop-up
mechanism.

Test 2

Attach a voltmeter to pin 3 (black wire with a blue strip) of the connector.
Operate  the pop-UP switch, you should see a steady 12 volts.
Attach a voltmeter to pin 5 (blue wire with a black strip) of the connector.
Operate  the pop-DOWN switch, you should see a steady 12 volts.

If this test fails, it's most likely your pop-up switch that has failed.  If
this test passes, and test 1 passes, then it's most likely the "passing
relay" that has failed
Turn ignition OFF, reattach the connector to the relay.

The relay is located under the left drivers side cowl a few inches up from
the floor pan.