Kind of guessing here, I will ask Chris to chime in with his experience once he gets back in town. But iirc there's a big doohickey full of lines inside the engine bay that runs the height control- similar to that spaghetti-looking thing they call A-Trac
It's in the way of your second battery, iirc.. the LC would just have an empty space there on the passenger fender. Then underneath on all 4 corners is another mess of tubes & some cylinder-type stuff, really no more complex than the wheel cylinder in your 40's drum brake, but again it's in the way if you want to add most off-the-shelf sliders.
In essence I'm not sure why it would add cost to lift an LX, but it certainly adds to the inconvenience when you need to remove all the AHC stuff. But the lift itself is just cranked-up torsion bars in front and some coil springs in back, plus shocks. Really no different LX or LC. Heck if you had some medium height 80 springs you're already halfway there.
82 fj40, 99 uzj100, 06 gx470
05 525EXC, 01 XT225, 07 TTR90, 07 CRF50