At this age, forbidding something is not going to work--she'll sneak if it is important enough to her. Instead, if you say yes, you get to choose the colors.
I don't think that she is too young but she really doesn't need to wear lip color at 13 because her lips are naturally plump and red. She would be better off just using lip gloss. If she is that intent on wearing makeup let her use a little mascara.
13 is the about the age when girls are starting to experiment with makeup. Lip color is a very good way to ease into tasteful makeup for younger girls. Target has many inexpensive brands that would be a good way to explore pink glosses and balms.
A little lip color is not going to hurt her. It doesn't matter if you accept it or not your daughter is growing up quickly and she's already a teenager.
You should let her wear lipstick, as long as it isn't distracting. She is growing up and there is nothing wrong with letting her explore make-up options.
Letting her wear lip color at 13 is a personal choice, however I recommend bargaining with her. For example, it will be alright with you if she wears a light, conservative color instead of bold. If she wants brighter colors, then just tell her no. This will give both of you an equal say and can avoid conflict.