Lots of lace patterns look like...ah...well, they look pretty wild and/or awful in the hand while we're working on them.
But after they're blocked, ah! then they shine. Reading the instructions for this lace scarf ("wonderful spring scarf" etc.), I see that one is to knit until the scarf is 60 inches from the CO; it will block to 70 inches!
That's quite a change. I'd say the curl you're experiencing will be dealt with in the blocking, as long as you're using a natural-fiber yarn. Are you? There are ways to make acrylic yarn behave, but I don't think it can be made to stretch from 60 to 70 inches....