I can't speak for Parallels as I use Fusion. The upgrade to Lion has had no impact on how Fusion operates. I use my Windows burning program whenever I can and it continues to function exactly the same. I use the free Ashampoo program or Nero as I do not like image burn.

Make sure that in Parallels, you have designated the optical drive as belonging to Parallels when the VM is running. It sounds like Parallels thinks the optical drive belongs to OS X. Either that, or your version of Parallels has not been updated to support Lion.