Binding dynamically to LGPL code is no problem for commercial projects at all. The only thing creating trouble is platforms where you cannot allow the upload of a new version of the LGPL code or where dynamic linking is forbidden. There all usage of LGPL code enforces the GPL or LGPL upon your code and all other code. Which you are most probably not allowed to do.
So you dont need another license using Mono as long as you are linking dynamically and do what the LGPL wants you to do.
Looking at projects using WebKit or Chromium solutions for browsing in a game. I have no idea how they do that, because when you use either of these solutions you will be using LGPLed code, its hidden in large parts of Chromium and its the license of WebKit.