It is better if you remove all the previous dye. The new color will not remove dye at all - you have to use the remover if you are going lighter. Since you did it a dark color, it may also take two applications of the remover, if one doesn't make it all come out. You can do the applications 24 hours apart if the first one doesn't make your hair color come out all the way . The idea is to have your hair all the same color before you put on the new color, that way it will come out all the same color and you won't look like a calico cat!
Just make sure you don't get it near your scalp!
Went from black to light brown. Went back to black. Went to medium blonde. Got sick of that and decided to do chunking and ...you get the idea. Granny's had a lot of time on her hands.