Certainly not for the transmission - the NAG1 / WA580 tranny uses synthetic fluid. Very different from the GM / Ford units.
For extra protection, a full synthetic isn't a bad idea - using the weight designated for the 3.6 engine.
Sorry, I wasn't that clear. My response was not an agreement the OP should use Lucas in his new car - like he has in his "other" vehicles -- only that he should continue to do with the new car what he has done up 'til now. With 108K miles on the engine/drivetrain and with no signs of any issues I think what ever he's doing is working. Don't fix what ain't broke.
Regular fluid services for both the engine and transmission go a long ways to maximizing component/system service life. The lubrication makers include whatever additives deemed necessary to get the most out of the lubrication fluid. Almost everything, and dare I drop the almost and say everything a owner can add to the fluid either is of no value or worse, could possibly be in some way harmful. Maybe only in a small way harmful, but harmful none the less.