Is it possible to tow a smaller aircraft (like a LSA with a non-functioning engine) with a more powerful towplane?
Yes.
I know of a pilot in the USA who has done exactly this.  Both aircraft were Cessna 182s.  The aircraft to be towed was outfitted with a releasable tow hook mounted on the prop shaft (I believe the prop was removed).  It took a lot of effort to satisfy the FAA that this could be done safely.  Part of this effort included videotaping towing a Cessna 182 (the one that ended up being the towplane) into the air via the same prop shaft-mounted towhook with a motorcycle on a long 7000' runway.  Since the motorcycle had much less engine power than a Cessna 182, this was evidence that the concept would work.
The end result was that the disabled plane was successfully ferried in this manner, with permission from the FAA.  I don't recall the exact starting point of the ferry flight but I believe the distance was in the neighborhood of 60 miles.
The ending point was an untowered field and as best as I recall the starting point was as well.
Naturally, the tow line was released before the aircraft entered the landing pattern.
This all happened sometime between 1990 and 2005; I don't recall the date more accurately than that.
If your LSA did not have a tractor (nose-mounted) engine, you might have more of a challenge.
A qualified glider tow pilot will be needed to fly the towplane.