Foxy Lady FATE question

I've been searching for her for a while and I found her today, she's huge and can be seen from afar. I started shouting for help, but before we could do anything she disappeared.
That was like 30 seconds from when I saw her.

Her FATE wasn't engaged, I didn't get close because I thought there were too few of us (3) and we'd need more help, but when this happens, will she spawn again in the next FATE chain cycle or does it trigger her CD (12~48h?) anyway?

Ya unfortunately it starts the timer again. Once she spawns you have 30 minutes to kill the fate regardless if you enter it or not.

Foxy Lady is truly not a cancerous FATE to spawn. As far as I can tell, it goes on it's year long CD regardless if anyone popped it or not.