Is Lheuton a legitimate character from TES or is it just someone that Tamriel Rebuilt made up for their project?

I've never seen that name before in my life.

Who?

I've never heard of him before, so he probably is.

Unless you mean http://www.imperial-library.info/pge3/hammerfell.shtml.

Lhotun is the newcomer in Hammerfell who wants to unite the Crowns and Forebears, right?

no, not really.

Lhotun has been around since Daggerfall, so he is hardly a newcomer. He is also not about uniting the Crowns and Forbears: his main objective is just keeping Hammerfell (mainly the northern coast directly under Sentinel's control) under his rule. It is for this purpose that he has appeased the Crowns in his population by being more respectful of their past. at heart he is still a true Forbear, the whole "omg new faction" thing is nothing but politics.

Okay, thanks. Does Lhotun want Hammerfell to remain in the Empire, or does he want to be independent?

He is well off under the Empire, and there is nothing to suggest that he wants to leave it. Secession is not as popular a view in Tamriel as it appears to be on the forums.