Yeah, that's the exact entry I found at thinkbabynames.com. I didn't really accept that, because Leith
is not really a variant spelling of Lethe (LEE-thee), but an entirely different name.
However, the similar pronunciation might explain why the name would be found on both sexes, better than to say it's simply a surname used as a first name (since Lethe seems likely used more for females). Although I'm not sure about that, either.
Another connection (via sound) might be with Letha
you tell me where (geographically) you met your Leiths, and roughly when they would have been born?