Think an LS can out handle a GT on a track??
Too vague. I assume you meant the new 5.0 Mustang GT. Cause if you meant Ford GT, then hell to the no. LOL
My opinion on a new Mustang GT 5.0 is that the LS would loose in general. It would probably be better on something like a slalom where the suspension and then tires is really what determines performance. I imagine it would fair better on hairpins and other lower-speed corners unpowered corners. The LS probably lets you brake later which should help your approach on turns.
But lacking an LSD, wider tires, and more power I don't see the LS doing better on much else. I think tires and an LSD would go a long way to closing that gap, but what the Mustang looses in speed to turn it makes up for in a hurry on anything remotely straight. Your only hope is that the design of the track doesn't allow it to effectively put down much of it's power, allowing a more nimble car to fair better.
If I were going to do a list of priorities to track a stock LS, they would be (and currently are):
1) Better tires (I got rims I liked too)
2) Front brake upgrade, including 320mm rotors, good pads, stainless lines (already done, as an interim measure)
3) Lower 1" with sport springs and Bilsteins (In process of collecting parts and time)
4) 8.8" conversion with LSD and 4:10 gears (Missing the TrueTrac, CV axles, and time to fabricate it all up)
5) Boost the 3.9L or swap engines for more power!
6) A big brake upgrade for real track use
Honestly, the biggest factor in who would win a race is the driver. A car can only do so much to help, or hurt, someone's times. But I am assuming we are removing the human element from the argument and talking about the cars only