First make your coach aware. As Gymmutti said, t may be that he/she has extras and even if not, he/she should know about it and let GK know about it. Maybe they will send another or give you a partial refund or something.
I have a sewing machine and do some sewing, but I would never sew DD's comp leo unless something came apart the day of the meet and I had no other choice. See if there's a professional seamstress in the area that you can take it to. Many drycleaners have one on staff. Hopefully you can get it done while you wait, or at least get it back really quickly. It will likely only cost you a few bucks (you can ask first if you're worried) and I personally would feel much better about letting a professional do it.
I can certainly see CoachP's point but I know my daughter would be horrified at the idea of competing in a different leo than her teammates. For me it would be worth shelling out a couple of dollars to get it fixed rather than having her deal with that. Besides, I don't know about you, but DD has 5 meets in the next 8 weeks, so even if it only takes a few weeks to get a new one (and knowing GK, it's likely to take longer than that), you'd have to wear a different leo for multiple meets.