I think Team Viewer is going to be laggy no matter what: it's effectively sending screenshots from your first computer to the second every ___ milliseconds, and unless you have a perfect connection between the two network lag is going to cause visible lag, as it just can't send enough screenshots fast enough.
The one caveat there is that TeamViewer doesn't really send the whole screenshot, it does some clever math to only send the part that changed ... it's just not clever enough. Other remote viewing systems might be "cleverer" and have better algorithms that improve performance, but still there's an upper limit.
While I've never used it for EQ,
NoMachine has the best performance out of all the screen viewing/remote control software I've used.