Surely they are basically the same engine. I'm pretty certain that the Beta marked the first time since being taken over that Lancia had used FIAT engines in 1.3, 1.6, 1.8 (1750?) and 2 litre DOHC format. In the Delta, the 1.3 and 1.5 SOHC motors were from the Strada/Ritmo and 1.6 and 2.0 DOHC units with 8 valves were simply developments of those used in the 131/132 and Beta.
The original Delta Integrale had the 8v 165 bhp engines and later upgraded to the DOHC ones at 185 (I think) and 205 horsepower.
If it's not an historic model, ie a World Championship car, I don't see that having a Coupe engine will make much difference.
I might be tempted to ring that garage in Northallerton (the name of which eludes me at the moment) and say you have a car without an engine and also a Coupe Turbo engine and ask if they would put it in for you. You could also ask if they think there would be any difficulties.
You don't have to ask them to do the work, you are simply finding out if the job is straightforward.