Haven't heard the LCD-X yet, but the LCD-3 can be very enjoyable with classical music. While very amp dependent, those lush mids can make stringed instruments sound great. And while the sound signature is very different from, say, the HD800's, the LCD-3 treble is not lacking. I have both of these phones and listen almost exclusively to classical. They are a great complement to one another.
That said, if you are looking for 1 set of phones to do it all, and you listen to a lot of classical, the HD800 and LCD-X should probably be auditioned prior to the LCD-3. If, however, you already have HD800's, then the LCD-3's are worth a listen, as they may just be different enough to offer a very enjoyable alternative soundscape.