As the mom of a 14-year-old who has no interest in makeup and hates the feel of it but does like to look nice, please, -- Ease your daughter into it. I would not do a makeover unless you ask her first if she wants one, and only if you are clear with her that you're totally OK with the idea if her saying no to it. Someone else making her up in a public place like a department store might feel a bit invasive to her -- I know some women love going to makeup counters for the full works for fun, or before an event, but really consider whether your girl (especially if she is a bit shy and if she has not already shown interest in makeup much) will do it because she really likes the idea, or because she wants to please you and thinks YOU want her to get a makeup-counter makeover. Also, if you go that route, bear in mind: You will have lots of products recommended to you by the makeup person and they will all be expensive, department-store makeups that cost a bucket; if you get them and your daughter never really uses them--?
I would either ask her up front if she wants something like that, or take her shopping for it at a drugstore and not a department store, or, my personal choice, give her a very nice little basket filled with a good quality, lightweight sunscreen, a couple of different lip balms (not lipsticks, girls this age don't go near it, it's all tinted or cleaer balms among my girl's middle school peers), a really fantastic hairbrush and comb (look at Bed, Bath and Beyond stores for lots of speciality brushes), some really nice hair accessories if she ever uses them (fancy decorated barrettes and ties that are nice but not so blingy she won't ever use them except once in a blue moon). If she wears nail polish for special things, get her a good clear one and maybe one other neutral color, or if she is into color, yes, get her something more colorful for her nails. But I would, myself, avoid giving foundation, liner, mascara, eyeshadow, blush, any of that. Not if she hasn't shown interest. She can feel very dressed up with new hair stuff, three or four lovely lip balms to try, etc.
EOS lip balms are very popular as you note and with good reason -- they're cute but also are 100 percent natural stuff. I prefer my daughter use those as they're basically just solidified olive oil, so no junky chemicals, and they have great scents that do not linger all day long!
I would also find her a fun book showing different hairstyles to try, if she has hair long enough to put up in different ways. There are lots of these kinds of books geared at young teens -- any Barnes and Noble will have them, with illustrations. Maybe a book about how to make your own spa items; my daughter was given a book that showed how to make things like bath salts, sugar scrubs, etc. from home ingredients and how to package them in fun ways to give or keep. Many girls are into being "natural" now and using natural ingredients.
I would not give makeup because of seeing other girls in her grade wearing it, unless she asks.