I wouldn't put cosplay and lolita together because one is a fashion and the other is a costume. You can't have both. Let's say you want to dress up as a character from Rozen Maiden. They all wear lolita styled clothing, but that would be a costume:cosplay.
You can, however, make a lolita themed outfit. Not a costume. I am currently making a Harry Potter inspired lolita outfit. I don't consider it a costume because I am focusing on the lolita elements with just a hint of Harry Potter throughout the outfit. But I suppose it is on the fence because I will be like a "lolita" HP student so that would be on the grounds for cosplay but still be a lolita outfit. Kind of confusing...
Also, if you want to wear lolita for a day, it isn't a costume. It's still a fashion. Like Meiki said, there's a lot of lolitas that wear their outfits to conventions. It's a great way to meet other loli's and talk about the fashion/brands/kittens/tea...
So I would suggest if you wanted to wear lolita I would do some research. You'd be surprised how much of a difference petticoats can make...There's tons of guides on livejournal and the Gothic Lolita Bible has tons of reference photos if you are new to the fashion.
If you just want to wear lolita for a day without really getting into the fashion, I would just end up cosplaying as a character that has a lolita styled outfit because there is a lot that goes into the coordination of a lolita outfit (and not to mention the subgenres of lolita:aristocratic, sweet, guro...) including time and money. If you really love the fashion and want to wear it for a day, I would recommend doing some research and if you love it, go ahead and wear it. You don't have to spend a lot of money on one outfit, but knowing what is lolita and what isn't will really help.
So... TL;DR- You can't have both, but you can under some circumstances lol
Mabel Pines-Gravity Falls
Next con:ACEN2017! ♡