Silent Install commands vary depending on the program itself and the installer they have used. Using /qn
will work for most (but not all!) MSI installers, as there is a Microsoft standard that most will follow, but EXE installers can be very different as they do not have guidelines like an MSI.
Searching for the name of the program and 'silent install' will likely bring up the programs help pages or a blog which lists the commands you will need to use.
A search for "lotus notes designer silent install" brings up this article which lists the command as:
setup.exe /s /v"/qn"
Which you would use like this:
Start-Process -FilePath "C:\folder\setup.exe" -Verb runAs -ArgumentList '/s','/v"/qn"'
Note: I can't test this as I don't use Lotus Notes, but it should work, or at least give you a good idea on what to do.