You have a P/N handy? I'm not wanting to modify the car, but that may be the only option in this case. A question I have is, Where is the mounting hole in the replacement truck? Is it in the same place as the one on the car?
There is one version of these trucks with silver side frames that is still listed as available on Lionel's parts site with (see below), which I have worked with. As Pete says, the coupler is at the end of a long shank which comes mounted to the truck itself. The mount is therefore to the metal frame of the truck, which will be a very long way back from the stock mount on the rear of the Lone Star car.
I think that these might have been originally a K-Line design and were used on 18" and 21" aluminum cars that had skirts on the sides but nothing across the rear of the car. To use them, you'd have to cut away (a large) part of the Lone Star car's rear skirt.
But I'm not sure that the replacement truck would mount very easily to the Lone Star frame, although both use a post and c-clip arrangement. These trucks also require a bracket that has tabs to fit into the frame (one into a slot and the other being screwed down), which was constructed to allow for this part:
The truck Pete mentions also used a bracket but not the same as the one pictured. Anyway, I mention this because I am in the middle of a similar exercise to fit a standard coupler to the rear of the Lone Star car and have decided to use a dummy with a slightly longer shank (I have one spare from a different project I can use). I am not keen to cut away part of the rear skirt although the car will have to negotiate O-72 curves.