I don't think you can marry Lydia. The marrying thing is only for certain NPCs, she isn't one of them from what I've played (and seen through gameplay videos).
Truthfully the whole relationship thing stupid, at least that's what I think. It seems like they just added it in, in the last minute just for the sake of it.
But for each their own. Hopefully mods help out with the whole marrying thing and they are actually worth it, at least from a story point of view. They can carry your stuff, that is the most usefulness I find for them (her) at the moment.