That type of lift just will not work on the LT, period. There is no lower frame for it to lift. Once you get the plastic fairings off, you will see that there is nothing but engine, transmission, etc., no straight, even frame rails like on a Harley.
One COULD possibly make several pieces to bolt onto the lift rails that would engage sufficiently strong points on the underside of the LT, but then you could not work on much of anything, because most of the work where a lift can be a help (it is NEVER a necessity) would require removal of something that the lift is attached to. That lift is pretty narrow, even if you could make it work, there would be a LOT of weight hanging off each side of it. Can you spell extremely dangerous?
I still cannot quite fathom why some feel that you cannot do much work on the LT without a lift. I had my transmission out more than once, and the complete engine once, never felt that a lift was worth the expenditure for the times I would use it. Then you have to store it 95% of the time you own it.
I pulled the swing arm and replaced the drive belt and pulleys on my son in law's Harley once, no lift needed then either. All that in my mid 60's. If I can crawl around on the floor, and sit on a mechanic's roller stool and do all that work at my age, why would I "Need" a lift? Doing all the work on my LT I did, I could see where the lift would actually be in the way part of the time, kinda reducing the joy of the times it helped.