Late period. Just came off 60 mg cymbalta (duloxetine) that I was on for a little over a year. Last month early period, this month late. Could the wothdraw withdrawal affect my menstrual cycle?

No, very unlikely. Minor menstrual irregularities are very common and are usually a result of natural hormone fluctuations .Cymbalta (duloxetine) has no demonstrable effect on reproductive hormones.
Probably not. But other stressors might . Was it ever really regular ?
Not likely. The antidepressants like the one you were on do not really interact with your hormones so I don't see this being the cause of your imbalanced menstrual cycles. Sometimes other factors such as stress can affect your cycles and other times you can have irregular cycles for no particular reason that you can tell. I wouldn't worry too much unless it continues for months in which case talk to your doc.