Generally speaking you need a glove box because lithium sulfate is hygroscopic, and it is usually found in the form of the monohydrate. (See for example the Wikipedia article on Lithium sulfate.) Especially the anhydrous material will quickly absorb water from the air, so you'll have some difficulty with accurate weighing.

If you are making an aqueous electrolyte you can just quickly weigh the amount you need and make your solutions, and optionally verify the actual Li(+) concentration afterwards by analysis. You can also estimate the weight increase rate of the powder on the balance and get an idea of the potential weighing error. If you're making an anhydrous solution however, for example in battery research, even a small amount of water can be a problem, so you should get access to a glove box.

I agree with Emanual Cooper, that you need dry box for handling of Li2SO4 because it is highly hygroscopic. However, Li2CO3 is not hygroscopic.