The function is similar, though LiveDictionary is a third-party application that can access many different foreign-language dictionaries (which is precisely what I need).
Here's what the developer noted in another thread about the issues involved
OmniWeb support isn't likely to happen, at least not soon:
The hardest part about supporting other applications is the code to scrape the text out of them. For things like Mail, iChat, Fire, etc., it's straightforward because they all use the standard Cocoa classes to display text.
Safari was a lot trickier, because WebView is a whole other beast. It took a couple of weeks to get text scraping from WebView to work, and a couple of months to make it work reliably. Other browsers use different ways to display the stuff on the screen, which is why LiveDictionary doesn't work in any browsers other than Safari.
OmniWeb uses a customized version of WebKit, which I assume is why it outright crashes, rather than simply failing to work. It should be possible to get a copy of their customized version and make LiveDictionary's scraper work with it, but it would be a lot of work and it's not a high priority.
This does refer to OW 5.1. Nevertheless, it could be difficult for LD to work with OW given what is mentioned above and elsewhere on the LD boards. Maybe Apple could create other dictionaries to work with their Services Dictionary (apple + control + d), which does work with OW.