I'm going to assume that this excludes the bare basics--things like petticoats, blouses, and so on. So I'm going to focus instead on the items I find to be interesting. Things that don't get enough attention, get the attention that they deserve but I still recommend, or are just versatile and good to use a multitude of ways.
Overdress by Dark Box (Taobao)
An overdress is a dress, usually without a proper skirt, meant to be worn--you guessed it!--over your dress. In the example from Dark Box above, the overdress (in black chiffon) is worn over a lighter-colored JSK. An overdress is a great way to unify an outfit, or to frame a print or old favorite dress in a new way. It works especially well with JSKs and skirts (OPs can be tricky--the sleeves may get in the way if they're too long, so be sure to try it on to make sure it looks right if you decide to wear it over your OP!). Using an overdress, you can turn that Alice and the Pirates skirt you've worn a hundred times into a romantic one piece look-alike! Overdresses can be made in sheer or non-sheer fabrics, so they can provide a multitude of effects, as well.
Closely related to the overdress are peignoirs (formerly robes worn over lingerie, they've been imported into Lolita from Cult Party Kei in the past year or so), and overskirts (far less unifying than an overdress, an overskirt is usually made of a sheer fabric; as its name implies, it's usually worn over a skirt to cover a portion of the skirt for aesthetic reasons).
Underskirt by Phantom and the Maiden (Facebook)
As you'd guess, an underskirt is the polar opposite of an overdress. Instead of being worn over the top of an outfit, an underskirt is worn beneath it! Underskirts are a handy tool used to lengthen a skirt by allowing the bottom few inches to show beneath the skirt worn over the top. This makes them an amazing item for taller Lolitas, or with one of those ultra-short Angelic Pretty releases! They come in a multitude of colors and plenty of different cuts, and some are ornate enough to be worn as a skirt in their own right (such as the Phantom and the Maiden example above). Additionally, with the falling hemline that's been a trend the past year or so, underskirts are a great way to continue to get a use out of your older, shorter dresses while keeping up with current trends.
Rose Combs by Rococo Soul (Taobao)
I'm sure it comes as a surprise to no one that I love roses in my Lolita. But really--flower hair combs are one of the best ways to add a splash of color or detail to make your hair ensemble just right. Need a splash more red in your coordinate to tie in your red shoes and bag? Add a red rose comb to your bonnet. Need to add a bit of texture and extravagance to a hime hairstyle? Flower combs will do the trick! Having difficulty finding a hairpiece to go with that country Lolita coordinate? Try a sunflower hair comb! Even worn on their own, they're a great simple accessory. They come in countless different flower types, and they're a super simple accessory to make on your own using tutorials like this one. You can even color them using floral spray paint, so you can always find the color you need for your perfect coordinate!
A Non-Shaped Purse
A/P Ribbon Bag by Alice and the Pirates
Given that Lolita is a fashion that is in part known for its unusual choice in purses (Angelic Pretty's pony bags, Innocent World's violin purses, and Moi-Meme-Moitie's bat bag come to mind), it may seem a bit odd that I'd recommend a plain bag. But honestly, a plain purse is one of the first purchases I'd recommend, and one that I'm somewhat regretting with my wardrobe currently. A plain bag will go with just about any Lolita coordinate, so long as the color matches. A shaped bag may look very out of place when the theme doesn't match up with the rest of the coordinate.
Imagine, if you will, a Gothic coordinate based entirely around musical instruments. You have Moitie's Harpsichord Trio OP, violin shoes, a few musical note accessories... and a bat shaped bag. Even though all of the elements are Gothic, the bat bag would probably look somewhat out of place, even if the colors match. This is because the themes of the outfit and the theme of the bag don't really match. Shaped bags are a great way of adding detail and unity to a coordinate's theme--but only if they match. It's best to buy something that can go with anything first, and keep it as a fall-back when you don't have the perfect purse for your theme!
Petit Ribbon short umbrella by Baby The Stars Shine Bright
I recommend owning a parasol for a few reasons. One: in summer, portable shade is amazing and super helpful, especially when in a fashion that traps heat like the multiple layers in a Lolita coordinate (this goes doubly so if you're wearing dark colors and/or synthetic fabrics that don't breathe well). Two: Parasols can make posing for Lolita outfit shots a lot easier, especially for newbies! And finally, three: A parasol can not only tie together an outfit, but it can really up your Loli factor. There's something romantic about taking a stroll in a park with a parasol on your shoulder--something undeniably Rococo. And isn't that what Lolita's all about?
I would recommend that you buy a parasol in the main color you use in your wardrobe (for example, black for a Gothic Lolita, ivory or jewel tones for a Classic, and white or one of the multiple pastel hues for a Sweet). This lets your parasol match more coordinates. A plain one with some ruffles or detailing is great to add some interest! If you'd like to up your parasol game, brands also release printed parasols from time to time, from full colored prints like this floral pattern parasol from Victorian Maiden to this sweet strawberry patterned one from Baby the Stars Shine Bright to monochromatic screen prints like this one from Metamorphose. But if you buy a printed parasol, remember that the colors and motifs in the print become a part of your coordinate, and should be coordinated appropriately!