No, you cannot directly interchange transmissions between a Lincoln LS and a Mustang GT without significant modifications, and likely not even then. The transmissions are completely different in terms of physical dimensions, mounting points, and even the type of transmission (the Lincoln LS used a variety of automatics and the 5-speed manual, while the Mustang GT used different automatics and manuals depending on the year). Even if you could somehow physically adapt the transmission, the computer systems would be incompatible, rendering the vehicle undriveable.
In short, it's a project that's far beyond a simple swap.
