This can be seen in a few different cases, but I always worry about skin cancer in white cats, so it's best to have it checked out by your veterinarian. I have seen similar lesions when they rub their nose on something, or with certain infections, so I would not be too worried; just have it checked to be safe.
It's not an emergency, but good to have her seen in the next week to ensure treatment is initiated early if it's something serious. For now, I do not recommend doing any sort of treatment at home. It's best to leave it alone until a vet can have a look.
Here is a link with more information about skin cancer in cats:
https://vcahospitals.com/know-your-pet/skin-squamous-cell-carcinoma-in-catsI hope that helps and all is well with Lily.