OmniWeb has been based on WebKit for a while. The problem is not the lack of WebKit, but rather that Omni makes a special build of it for their browser, with various customizations. Since LiveDictionary relies on certain extremely minor details in WebKit such as the exact location of certain function pointers, it doesn't work with Omni's builds. (This is incidentally why LiveDictionary sometimes ceases to function when Apple releases an OS update.)
In case Omni has dropped their customizations, or the customizations have become minimal enough that LD can work with them, you might try the "Make LiveDictionary Load in Mail and Other Apps" thread to try it out. Of course beware that it might crash if it's not happy with what's in there.