First off, there is nothing wrong with not wearing make-up, just as there is nothing wrong with wearing jeans and a t-shirt. Make-up is just another part of your outfit, making the overall flow more collected. So here are some metaphors for those cautionary about using it vs. natural beauty. If you do go the natural beauty route, make sure to take care of of you skin. It might take a while to find the perfect routine and products, but it will be worth it :)
Think of it this way: Your face is a sketch on a piece of paper, amazing and interesting and beautiful in its own right. Your face with make-up is anything from inking that sketch, using a light brush of water colors, or a full-on oil painting that takes hundreds of hours. The sketch will be up over the painting in some circumstances, and the painting in others. To take my metaphor even further, you usually won't use a very plain frame (clothes), for an oil painting (face) or the opposite - it just wouldn't match (Unless you're trying to make a statement or have an amazing sketch, but that's not part of this tl;dr).
So hopefully you now know the reasoning of wearing make-up with lolita, and maybe you even want to try wearing some. Here's the big problem: you go to the drugstore, buy some Maybelline, put it on, and your face turn into a puffy, acne mess. You come to the obvious conclusion you are allergic to make-up, but it's less an allergic to make-up, and more allergic to the ingredients. And even if you are sensitive to foundation, try having fun with other types of make-up.
You still want to use make-up, so you get into the mineral make-up trend. Better, but still no - this is because not all mineral make-ups are created equal. Your most likely problem is that whatever you're using has bismuth oxychloride, which among other things cause acne and irritation, and parabens, which can cause irritation, contact dermatitis, rosacea.
That build up leads me to point you to the The Cosmetic Safety Database. This ranking system should be taken with a grain of salt, but is a great starting guide, because it not only rates a products toxicity, but also the irritating ingredients. But don't restrict yourself to things only listed in there, but use what you learn from CSB and other places to go to for more information, and apply it to the ones you're researching.
So! Here is where I give out some brands for you to try. This stuff is generally expensive, so always order samples of even the most obvious things to make sure they work for your specific skin type before wasting your money on something you won't use. As I first post this, there will be only one (I was extremely lucky and found my ideal line after a couple days of searching), but hopefully other will contribute their own reviews :)
Zosimos - I love this for many reasons, from a wind-powered production facility, the variety of types of products, and the constantly expanding collection. There is a good selection of foundation colors in varying under-tones, although I think the primer causes to me to break out for whatever reason. For lolita, the setting mists creates a nice dewy look.
--lip and check tints: I love these, because they're not only great for their versatility, but because they provide that 'natural beauty' lolita look with a hint of color.
--blush collection: Amazing selection, and even me who's ghostly pale found one I like.
--eyeshadow: They're very buildable, meaning you can either go for a light, barely-there application (Which seems to be very popular in the GL bibles for sweet lolitas) to something foiled and intense (Something more appropriate for gothic lolitas)
Another thing I would suggest, even though I haven't used it, is Afterglow Cosmetics. Check out their drop-down menu "New to Minerals?" and "Advice" :) And if I won the lottery, SukiColor >.>
So, would anyone like to give their own sensitive skin (Or even non-sensitive skin) make-up reviews? Your personal lolita look? Tips? Short tutorials? Youtube links? I want to make this something informative not only about make-up, but how it can be used for lolita :)