You don't really need to exercise the 4×4 Low setting. The main thing is making sure the 4×4 drivetrain gets used every once in a while. That will keep it functioning.

I wouldn't drive it in a parking lot. You'll start binding up the drivetrain when you turn and risk damaging stuff, or get your drivetrain stuck in 4×4. Find a nice, straight road, put it in 4×4 high and drive straight for a few miles. Turn off the system before you make any turns. 4×4 can wreck itself on dry pavement when you make turns with the system operating. Driving straight does nothing. A friend does that in his F-150. 

I would not monkey with any 4x4 system regardless of the manufacturer. If I need to use the 4LO function or even the 4HI, I'll use it when I need to. Leave it alone.

Posted by: @gxowner2000

Hi, I just bought a brand new GX

what's a "GX"?

Posted by: @gxowner2000

should I run the car under 4LO mode a few times a year

well you either need to use it every year, or you bought the wrong vehicle.

I have a GX470, From what I remember, I haven't checked it in a while, but the manual says to put it in 4x4 and drive it 10 miles a month.

Where I am at , I drive it every now and then, maybe not every month, in 4hi for probably 5 miles, and then I use 4 low, especially when going down some crazy hills on a bad dirt road, but probably for maybe a mile or so. The things are so capable even with just the awd, I don't often find myself needing it, but sometimes it sure comes in handy. I want to make sure it works when I need it.

As was mentioned before, don't do it on dry pavement.

Posted by: @gxowner2000

should I run the car under 4LO mode

as far as I can tell, the four-wheel-drive is a full-time system with a center worm gear differential (more like AWD) so it's constantly working anyway.

As for the electronic low range... maybe just cycle it on and off now and then so the shift motor doesn't get stuck.