Lateral work always helps a stiff horse. Having the horse step under himself with the rear leg will be step one of the two step process that brings a horse's weight momentarily onto his hind legs. Take your horse on the halter, stand in front of him look at his inside hind and while backing him , focus on making that inside hind STEP UNDER and to the inside (right under the mass of his belly) When he does this you should see a very slight "lean" of his whole body rearward as he puts weigth onto that inside hind and the next step will be outside hind stepping over. If he has really rocked back onto his hind legs, then you can ask him to step his inside front leg over (to the inside, or same side as the inside hind was on). THis is an excellend excersize for softening a horse.
If your horse gets stiffer during lateral work, you may be "freezing" your aids when asking him to step over. Your lateral aid needs to be times with his inside hind stepping in/over (just like doing it on the halter) and your leg pressure comes on and off as the horse steps over. It is like your aids for lateral movement must "breathe" with the horse as he rythmically steps over.
Get two steps over and then let the horse move forward.
That would be my guess as to why your horse gets tens in lateral work. Like I said in an earlier post, if the horse gets tense, don't try to corral him inside TWO tight reins, have one active rein and one supporting rein and the contact can be different. That helps the horse not feel the need to resist. And in the extreme, if the horse was totally running through the reins, you would drop the outside rein and pick up the inside and really bend the horse around until the hind end steps under and the "engine" is derailed from the tracks. The so-called "one rein stop".