The first thing to do is to "trace ports" from the workstation to the server. It's in "File..Preferences", under "Notes Ports". This'll tell you if there's a passthru attempt, or some other delay trying to get to the server.
If you can see the time delay occurring while tracing the port to the server, with no passthru attempts, and no other attempts to contact the server by a different method -- that is, if everything's quiet, but the connection takes a long time to establish -- then upgrading from ADSL is likely to help your user.
Opening a database does take some time if you're doing so in LotusScript. Opening with a UI object takes even more time, because you may be executing more than one connection, depending on what launch setting you're selecting, what your Database Open script does, and what the frameset or navigator does that you're opening.
If you're opening to a view, it's important to take a hard look at your view design, too. It shouldn't select documents or calculate columns using @Now or @Today.
There're less obvious time sucks as well, but these are the more common ones.