Haven't done this with the LS, but I have done it with my old 89 Taurus. The sunroof gasket looks very similar. Working on the sunroof is much easier if the glass part is removed from the car. I think there are 4 or 6 screws that hold it in. Don't force the support bars, they should come out pretty easy.
Removal on mine was pretty easy, it is just glued on, so you find a loose end and peel it off.
Clean the edge of the metal frame very well. I think my kit had a cleaner cloth with it. Wash your hands so ther is no skin oil to contaminate things while working. Maybe even wipe your hands with rubbing alcohol, not that gel stuff since many of them have oil in them to moisturize.
Read the instructions carefully. Each kit may be different. Some kits have a two part glue, others just work with the glue preapplied to the gasket. Following directions just apply the gasket with even pressure and make sure your hands and the metal surfaces are squeeky clean.
The one mistake I made was that while applying the new gasket I stretched the rubber a little bit, that was dumb, what stretches also shrinks, duh. I cut off what was left and threw it away, mistake. After a day or two I discovered that my gasket had shrunk about 1/2 inch and left a gap. So when you do this job be very careful you do NOT STRETCH the rubber. And save whatever piece you cut off incase you get a gap later. In a pinch, foam rubber gasket from the parts store will work to seal the gap if later you get one.
When you close your sun roof make sure the gasket is not pushed out of place. Having a helper close the roof while you watch is good. Let it sit a day or so with the roof closed so it seals.
Good Luck, it is much easier than my long winded description leads you to believe. The critical parts are cleanliness and no stretching.
Jim Henderson