This is probably going to spark some controversy BUT
***NOT ALL LACEWEIGHT YARN IS SUITABLE FOR KNITTED LACE***
so... what yarns are?
Well you want something which is:
- not too fluffy but with some halo
- fairly solid in colour
- not too soft so it pills while knitting
Something fine is more than 800m/100g. Something elastic is most natural protein containing fibers including wool,mohair, silk, cashmere, qiviet. Non-elastic fibers include cotton, synthetics such as nylon, acrylic etc and semi-elastic ones include alpaca and wool/synthetic blends which are generally best avoided. However these can be used for a specific purpose such as cotton for knitted tablecloths and with very careful swatching.
A good place to see how some different lace yarns behave is here
Lace yarns I'm particularly fond of include:
Rowan Kid Silk Haze (but this is a pain to frog)