Lizzie is Ciel's first cousin, don't forget. He doesn't really care for her in that sort of way, he just left the marriage arrangement alone since a) it was too much of a hassle back then to get it annulled and Ciel is a bit lazy. b) probably some sentimental value given that it was arranged by his parents and aunt. c) He doesn't expect to live long so why bother with it. and d) Since marriage to a relative becomes illegal in early 1900s, Ciel and Lizzie would probably have to get a divorce if he does live that long. (And let's not forget the high risk of birth defects).
But yeah, Undertaker could have something to do with it. She is his cousin, and his Vincent's niece.
My guess is that it has something to do with the fortune teller guy. If he has any connections to Undertaker that's what I'll have to wait for.
I'm pretty sure undertaker has something to do with Lizy's disappearance. Lizzy is Ciel's finance, and for some reason Undertaker is obsessed with Ciel, so he might have done something. Also P4, those boys are crazy, and you know they had something to do with it or they wouldn't have been brought back into the plot. in this manga, everything happens for a reason