I can speak with authority on this topic as I've swapped gen1 and gen2 LSs to manual conversions, superchargers, and 302 engines. Your will not be able to do this conversion. Especially, because you missed the small detail that a 96 SN95 V6 is a 3.8. 3.9 V6s were only available in the 2004 Anniversary edition new edge Mustangs.
The bell housing on the 4r70w is integrated into the transmission and it uses a Ford small block Windsor bolt pattern (yes same as 3.8v6). The Lincoln LS uses a Jaguar bolt pattern. Completely different, not even closely related.
Additionally, the LS has hundreds of settings in the PCM that would have to be disabled, as well as multiple codes to shut off the CEL. Also, the LS has about 13 modules that communicate on a bus that cannot be modified. This swap will affect things like the gear selection indicator on the cluster, the car recognizing it's in reverse, or the traction control recognizing the transmission, or the drive by wire system accepting the selected gear, speed and anticipated torque.
Your best bet is to get and SCT tuner and use a canned tune. They adjust for throttle response and shift firmness.
This is easy and much less expensive. Also, you'll like the throttle response.
Dennis
