Who says that lace has to be knitted in superfine laceweight yarn?
Yes, that will create a a very fine floaty item, but it isn't the only way to knit lace. You can use lace pattern in any yarn - for example this top I designed for Knitting Magazine features a lace pattern knitted with two strands of a cotton bamboo DK.
In fact if you are completely new to lace, I recommend going for a DK or a 4-ply pattern so you can concentrate more on getting the hang of the techniques than worrying about tiny needle or seeing fine yarn.
And while I generally say lace can be worked in any yarn you like, I would recommend avoiding something hairy like mohair for an early lace project because it is harder to see the lines of decrease and it can be a real pain to unpick, and most people will find the need to unpick when starting out with lace knitting.
If you need help with lace or any other knitting techniques, I can help. Find out more here.