A gorgeous, heavy pattern goes well with a light and sweet dress like this. Earthy colours bring some variety to sometimes overwhelming brightness of Lolita fashion; a classic style is more toned down, if not more mature, than the major part of Sweet and/or Gothic Lolita.
Pale shades of pink (as shown) and blue would probably work the best with the brown there, perhaps antique white as well. I'd recommend one didn't overcrowd the ensemble and keep all other elements low-key, free of adornments.
This dress comes in various patterns and colours. View it here.