It sounds as if keloid scarring may have occurred. If that is the case, I would recommend seeing a medical provider to treat the scar prior to starting laser tattoo removal. Typically, keloids require steroid treatment, either topical or intralesional. Once treated, laser tattoo removal should be effective.
It is likely that the skin will remain raised and thickened. Also, if it has been tattooed more than once, it is likely that some of the pigment may remain.