I have two tattoos, so I've been through aftercare procedures twice. This is a combination of my experience and research on aftercare for tattoos.
First of all, many tattoo artists specifically recommend against using traditional, lye-based soaps on fresh tattoos. Messing with the pH of healing skin is a bad idea and you want to be really careful not to dry out or over wash the new tattoo. I used a clear, gentle, fragrance-free hand soap and put ointment on it the first week, and fragrance- and lanolin-free lotion for the rest of the healing time.
If you decide to go ahead with a soap for her, it should have absolutely no fragrance or essential oils. And you need to know everything she's even slightly sensitive to because any kind of skin reaction will alter the color of the tattoo. Honestly, if you've made a soap for her in the past that she's liked, I would just use that, minus any scented ingredients. Also, no exfoliants. Basically, you want to be as gentle on the skin as possible, so no clays or salt. If your friend hasn't already been using your handmade soap, I would advise against her starting on freshly-tattooed skin.
And obviously, she should ask her tattoo artist for his or her recommendations to help advise you as well.
