If you're building a completely underground station there is no particular reason why it should be under the old union station. Placing it under the CBD would work far better for the riders - you might even avoid it having to go above or below the LRT tunnel. Also, for commuters going further on the LRT, right in the centre of the line would make sense for people taking the LRT for the last portion of their trip, to Tunney's for example, without trying to crowd onto a full train.
The reason why I figured Union station would be a good spot to put it is:
1) It could be built under the Canal and Colonel By Drive (ie no building foundations to deal with, except for maybe the tip of the NAC)
2) The land already exists south of the 417-Nicholas interchange to have both a tunnel entrance and a bridge directly to the existing tracks.
3) It would be by far the shortest tunnelled route into downtown (nearly exactly 2km).
4) It would be a symbolic renaissance of rail-based transit in Ottawa. Using the old rail station as the new rail station.
Yes, the walk for some would be a fair distance, but build a couple underground walkways and that trek becomes less of a hastle during the winter. Also, it wouldn't cross the LRT tunnel at all. The LRT tunnel would be directly east of it, and would swoop across and come in just north of where the tunnel would end.