I bought a used 2009 LX570 with very high miles and the 4 lo wouldn't engage. Here's a brief synopsis of how I got it to work.
Attempt 1: Shift switch into 4 lo (while in neutral). Got !, ABS, VSC lights, 4 lo light blinks. Got VSC malfunction message on MID. 4 lo is not engaged. Multiple switches (while in neutral to 4 hi to 4 lo back and forth). Would not engage. Switch back to 4 hi. Drives fine, but all the lights stay lit. Turn engine off, lights are gone after turn back on (about 15 min).
Attempt 2: Shift switch into 4 lo (while in neutral). Got !, ABS, VSC lights, 4 lo light blinks. Got VSC malfunction message on MID. 4 lo is not engaged. Rolling in drive, then reverse a few feet. Multiple switches (while in neutral to 4 hi to 4 lo back and forth). More rolling back and forth) Would not engage. Switch back to 4 hi. Drives fine, but all the lights stay lit.
Go buy gas (forums say these lights could be result of gas cap pressure/fit). Lights don't go out after fuel fill (engine off during fill). They do go out next long engine off (approx an hour).
Attempt 3: Read many forums. One tip is to move switch to 4 lo and turn car off. Then 4 lo would engage on restart. Attempt this. Same lights on 4 lo switching ( !, ABS, VSC lights, 4 lo light blinks. Got VSC malfunction message on MID. 4 lo is not engaged.). Turn off. Wait 10 seconds. Restart. Hear solenoid and 4 lo engages immediately on restart. No lights on dash except 4 lo solid. Success! Roll back and forth a few feet. Try out crawl control, etc. Car switched in and out of 4 lo two more times no issues.
What was the cause? Probably just a sticky solenoid.
Forums indicate other items to look at are: a low/faulty battery, faulty 4wd ECU, or faulty switch. My service records show a 4 lo solenoid replacement less than 10000 miles ago, so if it happens again, I'll have the battery tested.