Technically it is grammatically correct, but the way it is worded sounds weird because the two "lasts" are so close together. Personally, I prefer my example above, but that's just me. Maybe someone else has a different opinion.
It does not sound at all odd to me to use "meet" to mean "encounter someone, and not just for the first time". I would think it perfectly natural to say:
I met my mother in front of the drugstore.