I was thinking that offices with monitors have those nasty fluorescents with the grills
They also use up lighters and wall washers that reflect the lights off of the walls and ceilings (probably no good for you but it shows that reflections and glare is a problem with monitors)
I don’t know what you both have in mind; hopefully someone else will have some suggestions
But here are my thoughts
Just a couple of ideas for you and your customer to think about
Will your office look anything like this?
I was thinking maybe your built in light boxes for ambient lighting?
How about a bookcase light for some task lighting? The top cabinet should keep reflections off the monitor
I would have a play with various lights combinations and angles especially if you have a few odd lights hanging around
Hope I am helping and not making things more confusing