I do NOT know if this is true for the LS, but some of the older Ford horns had a cheesy metal(thin aluminum sheet?) sandwich with dimples separated by some foam with holes cut in it for the dimples. When you press the horn, the metal sandwich deforms and allows the dimples to contact thru the holes in the foam.
Maybe this is how the LS horn works.
My 89 SHO had this kind of horn and it once got stuck on. I was on the freeway in traffic and had just beeped the heck out of someone and the horn stuck on. I peeled the plastic cover off the horn pad and discovered the metal sandwich arrangement on the fly, down the freeway that is. I just bent the part that looked too bent back into shape and the horn stopped. It was easy enough to do that I was able to do it while in traffic and in a panic.
A free fix, my favorite kind, if this is the way your LS works and if this is your problem. Before replacing the clock spring I would do a resistance check on the connection from the horn pad. Normal should be infinite or very high resistance. Stuck would be near zero. You don't want to mess with the clock spring unless you are sure that is the problem.
Good Luck,
Jim Henderson