So to shift to four low you stopped, placed the transmission in neutral and then pressed the button to select four low. Correct?
If it did not work properly, the first trick I would try: Reset. Disconnect both battery cables. Wait three minutes. Re-connect both battery cables.
If it still doesn't work...the suspect on the top of my hit list would be the encoder / transfercase motor.
If you are handy and wanting to spend some time checking other things you can check to make sure the front axle actuator is moving, has vacuum (no rotted hoses) and the cable is not stuck or broken. You mentioned lubing it. I assume it worked fine then? The front axle actuator and assorted parts won't keep the transfer case from shifting. They will keep the light flashing though. If it did not go into low range, that is all about the shift motor on the transfercase. It is possible the switch or the module are at fault, however you still have lights that function and they are trying to do something. If the reset did not get them going again, it seems to me that we are right back to pointing at the transfercase motor.
Mine on the Avalanche went out at under 100k miles. I have seen a couple more go around that mark too. Pretty easy to change. Pretty pricey part though. When it comes time to go get one, be sure to count the pins on the electrical connector before you go. There are a few to choose from. Reman units run about $170. New $224
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