I would not substitute crochet cotton for worsted weight yarn,especially when the pattern calls for a certain wieght,it's usually because the gague for the design calls for it.
I'm surprised the pattern calls for that weight for a lace design,usually lace patterns call for a fingering weight,or lace weight. There are so many beautiful lace patterns for sweaters etc.
Be prepared however, for a whole new type of knitting experience. Lace designs depend on using a chart and careful attention is needed to keep the pattern correct.