So here's some simple tips on how to stay relatively cool while still retaining the lolita aesthetics.
Wear a short-sleeve blouse under your preferred jsk
I myself am especially fond of Innocent World's short-sleeve ecru boleros. Not only are they breezy and light, IW make 'em in L size too.
Eschew a blouse, cardigan completely
Now, this is slightly trickier because not all lolita dresses can look good by themselves but there are quite a few that can.
A sleeveless dress that already has a collar can help make the outfit look less 'bare', while halter-necks are always good for that summertime style.
Pin your long tresses up!
It can compliment your overall look and also leave the neck cool.
Invest in a sturdy parasol