I also have to wear an ID badge to work, but I hate lanyards. I really don't want two competing things around my neck.
I have one of those clips with a retractable string, and my id badge in a clear pouch at the end of it.
I clip it either on my waistband or beltloop, or to the side of my collar or neckline away from my necklaces. If I wore a jacket I would clip it to a top pocket or wear it around the collar and the pearls around my neck.
If you look at the Show Us Your Pearls thread, you may see photos of me with my ID badge that might give you ideas.
As long as your lanyard is soft fabric, it won't hurt the pearls, but I wouldn't wear them with a metal lanyard. Although many people do wear gold chains and pearls and no harm done, but gold chains are usually very fine and gold is a soft metal. I think a Brighton lanyard would have a much heavier, harder metal chain, and I wouldn't mix it with pearls, but there may be ways to wear both if you are wearing a collar (lanyard outside the collar and pearls inside the collar).