This is possible, however there are JL's all over running between 2 and 4 inches of lift with no complaints of bump steer except you. I suppose your aftermarket axle could be the difference.
All of these things can cause poor handling and maybe induce death wobble but to the best of my knowledge not cause bump steer.
Perhaps your definition of bump steer and mine are different, either way good luck with the repairs.
Just a little background...I am a bit picky and also a bit OCD. In a previous career life I was an ASE certified line tech at a large Chrysler-Dodge dealer and later a Mercedes tech, shop foreman and then Service Manager for one of the largest Mercedes dealers in the Southwest. I have also driven a few friends lifted JL's and honestly there is NO way I would accept the way they drive/handle on the road...Mostly due to sloppy workmanship, mismatched components and/or tire choice.
My goal is to get my JLR with a 2.5" lift and 37" KO2's to handle on road as close as possible to how it did previously with just a 2" lift and 35"KO2's...I think 35" tires are the sweet spot for a 2-door JL, she ran smoothly down the highway at 85mph tracking straight as an arrow, had no bump steer and performed outstanding off road on our dry rocky Arizona trails...