if you have to give out an unlimited, royalty free license to your work, I think it's not unfair to say that you have given up your copyright protection. As the copyright holder, it's true that you can relicense it to suit other licenses, but it's not clear to me that you can clearly make a copyright infringment case if there is an LGPLed copy in the public.
Well if somebody uses my work in a way either not permitted by LGPL or explicitly permited by me through some other license I can't see why I can't sue.
But the point I'm trying to make is that I can be in violation of your RELICENSE. I can make a claim that YOUR work is covered by the *GPL, so that your RElicense to me doesn't apply. If this holds, then my original statement that you gave up your copyright protection holds.
-r