That's all I can think of. I may be a huge history geek, but those battles were extremely famous and, to an American, anyway, probably the first thing that "Lexington" brings to mind. I can't imagine it as a name for a person; it's "the first battle in the American Revolution" to me.
Also, I tend to find -ington names in general to be annoyingly pretentious, although
Lex is a decent nickname.