This is my favorite one... You're not getting full throw of your linkage because the lift cocked the linkage .. There is a 13 mm nut on the linkage rod...loosen that and have someone hold the lever up while you manually put it into 4 low you will fill it solidly shift in and then secure the nut.
If it's a manual rotate the lever on the transfer case toward the rear of the Jeep while the nut is loose and handle is up..this sets you to a baseline , fully engaged , handle up position , and the rest is typically fine (neutral, 4-hi, 2-hi) ...the closer you are to 2hi the less throw is involved so the shortage you have now isn't a factor .
if you go to a cable system you will be really happy and won't have any more issues but that should solve your problem right away.
What you don't want it partial engagement , then it pops out .
There is a plate Rugged Ridge sells to correct this , but a Savvy cable is indifferent to the transfer case and body relationship and takes all the linkage issues out of the equation.