Is it safe to lose weight from vomiting in 1st trimester?

Depends. I always tell my patients that worry about things you have control over. You don't have control over your weight loss if it is from vomiting so just do your best to avoid triggers that cause this. I had a patient that lost 35 lbs and then when the vomiting stopped, she gained that back and another 50 lbs and had a healthy baby. I hope this helps you in some small way!
Never. Bulemia is never an appropriate way to lose weight, particularly during pregnacy!

Related Questions

Would if be okay to lose weight in 1st trimester?

Probably but don't. Your baby is drawing nutrition from your body and losing weight is best postponed until after childbirth.