MTM is always based on the Lazio/La Spalla fit. Even if you choose different shoulders or lapels, it is still going off the same block. You can change most measurements and adjust for shoulder slope etc.Perhaps someone with greater experience can comment but outside the US (specifically in Australia) the MTM/MTO service doesn't seem to be based on a specific block: one can select any combination of shoulder, lapel width, and button constructions. I looked at my invoice for my order and it makes no reference to the block that was used although in the US it seems that the Lazio seems to be the base? When I got measured the SA used a Havana fitting jacket and I would assume if I had wanted different shoulders he would have brought out a different one?
You could make a custom jacket based on any other model, like the Havana, (atleast you could, not sure if it's still available) where you can change some basic measurements (jacket and sleeve length, waist, etc.). You can change fabric and buttons obviously, but not alter design options like shoulders or lapel width.
If you look inside the jacket on the tag, it's going to say which model it is based on.