That depends on the program sometimes. Especially true if it uses the same files when run over the network.
Normally all you need do it allow access over the network to specific directories and a computer. Than when the other remote/LAN computer either attaches a network drive or uses Explorer to get to the folder, it can run the EXE. Problems can occur though depending again on the program. If it needs to access the Registry say to verify you have a legal license, that license resides on the host computer, not the remote one you are trying to run it on, and that license is NOT in your Registry. Same would go for some install files possibly. Many programs are 'self-contained', that is all required files except for system files are on the folder and sub-folders. However, some installs place files in the USER folder or WINDOWS folders... and in these cases running the program over the LAN will probably fail as you are missing them.
Best to just try it and see.
As for the other user on the computer you attach too, well, if a game it could be problematic. Some save INI or progress files, so you can't have individual ones, or in some cases, to stop multiple instances of the program from running, they open files with 'deny all' and the 2nd instance of the program can't open it and fail. Why not just install (and pay license fees if required) on both computers?
Again, just try it and see what happens?