Is the fur licking a new behavior? Have there been any changes ----in your routine, new house/apt, new dog/cats outside, new noises? Lulu sounds like a needy cat, and if there have been any changes, she has started "obsessive grooming" This is something quite a lot of cats do to soothe themselves, if they are a little upset about something. Zuba had lovely curly hair on his tummy until we had three months of indoor renovations done in our house with all the hammering, drilling and noise that go with it, and when the renovations were finished, Zuba still kept on with the over-grooming, and has never
grown out of this habit....so he has a bald tummy. Unfortunately, our younger Devon picked up the habit from Zuba even tho there have been no changes at all in our routine, or any work done. You could get something from the vet to make her feel calmer. Another thing you might try is Bach Rescue Remedy
; it works for some, not for others, but worth a try. Bach Rescue Remedy Pet
As for her vomiting, have you changed her food? You should have her checked out by the vet for this, as it could be something serious. All the best!