I have lemon balm plants in two different gardens in two parts of town, and even though the plants are alive and growing, I can never tell if they are thriving. I keep moving them around to be sure they are not getting too much or too little sun, but they keep getting stuff on the leaves. Either spots or what appears to be fungus or... Maybe the soil is too moist?
Make sure they receive a lot of sun during early morning and early afternoon, since the midday sun might damage them. They also grow best in a wide patch of fertile soil that can drain easily, so I recommend placing them in wide and short planters.
In my experience, when it is very hot lemon balm likes frequent watering(as in it starts withering), but after I water a very withered lemon balm plant, within 45 minutes it looks brand new again. NONE of my other types of plants recover this quickly from drought.