First I want to start with just a little bit of musing about why certain colors are considered "unusual" in Lolita. Generally, Lolita tends to be a very rule oriented fashion, and there are colors that are often perceived as being not just "normal" colors for Lolita, but sometimes they're considered the only acceptable colors, although, this has lightened up a bit in recent years. "Proper colors" seem to be largely decided by what sort of things brands are releasing, and as silly as it sounds, it's usually for an understandable reason. As I'm sure you all know, a head-to-toe matching outfit and even wardrobes is not uncommon at all in Lolita, and is even something that most Lolitas prefer, so it's generally just considered easier for Lolitas to pick one of the common colors and stick with it. It's easier to match that way if all of your clothes just so happen to be pink, sax blue, lavender, red, or black! It becomes a little less easy to find exactly what you're looking for when you throw every other color into the mix! It's a bit unfortunate for those who have very specific color inclinations, but a blessing to those who don't really intend to stray very far from the limited Lolita rainbow.
However, it's true that in recent years more and more colors have mixed themselves into the Lolita norm. I remember about 6 years ago a Lolita friend of mine was in love with the color green and dreamt of one day owning all the non-mint green brand released Lolita dresses. This was a pretty easy feat at the time, theoretically, as there were only about a dozen or so of them that were commonly known (Take a look at this search for "Green" grouped by year on Lolibrary!) . For the next few years brands started releasing more and more uncommon colors, and there was always a little bit of a murmur of commotion every time a brand released something in an odd color. "Did you see that yellow dress?" one Lolita might ask another, "Yes! Did you see that one that had mint and pink on it!?".
Nowadays, there are very few colors that Lolitas would ever be shocked to see, except maybe neon, but there are indeed a few colors that are still very underrepresented and often overlooked within the fashion!
Jewel tones that aren't burgundy or royal blue