My brother, I think I mentioned, has been on the Lithium for 30+ years and will be for life, he accepted that awhile ago.
Well the reason for this reply, is to let you know, the summer is not as huge as a big deal. His doc told him to be sure to drink water if he is working out in the heat or in, he lives in NC, summers get pretty hot.
His doc never encouraged him to increase dosage due to heat.
Mine didn't either, just to be sure to keep hydrated, naturally not over hydrated, I mean like drinking as a camel, ha!ha!
Once a good level has been established many pdocs will not want to mess around with dosage of Lithium unless a little fine tuning is needed, so increasing for warm season's sake, I personally do not think it would be good unless the pdoc periodically is doing bloodwork, monitoring kidney function, etc. I had a professor who also was bipolar, didn't have dosage changes during the summer but always had a beverage with him in our classes during the warm weather.
Well, enough of my chatter.