yes, find a way to shimmy them if you can to take up the excess slack. a washer, or a piece of plastic or rubber, something thin enough will be key, but soft enough to not score your lever. let us know what you come up with!
First, remove the lever pivot bolt and grease the living daylights out of the whole pivot assembly. If the vibration goes away just keep it thoroughly lubed and you're good. In any case more lubrication is usually preferable to less, so what do you have to lose?
The best way to take up free play is to find a piece of thin felt (synthetic works here as well), cut it into a washer shape, thoroughly work in some general purpose grease, and then see if it can be worked in between the lever and the lower face of the perch without damaging it or causing excessive drag -- the last thing you need in a lever.
I've even used a greased scrap of t-shirt for the same thing, but it shreds pretty quickly.
On the other hand you could just ride it and ignore the vibration.
If it has already been done, it is safe to assume it is possible to do it.
On the other hand, if it has not been done never assume it is impossible to do it.
------- Rob --------