Dd started doing this very young, maybe 1.5, her lips definitely get dry but the picking is a comfort thing, she's practically in a trance. I constantly remind her to use her chapstick (lip stuff). In fact it's now her favorite thing to buy at the store. She ruins them, loses them and always has several 'in use' but whatever, it helps.
Mama to dds, Juju(7) and Bea(4)