Most homemade lemonade goes wrong in one of two ways: it puckers your face, or it tastes like cold lemon sweets. The fix is not a magic recipe. It is one balance between two numbers, how much acid the lemon brings and how much sugar you add against it. Once you can see that balance, you can make lemonade in any size, any sweetness, with a lemon, a lime or a mix.
Lemon juice is mostly water with a lot of citric acid. Published measurements put fresh lemon juice at roughly 5% citric acid by weight, so about 5 g in every 100 ml, with lime juice close behind. Sugar is the opposite force: it softens the sourness and adds body. Your tongue does not read "5 g of acid" or "9 g of sugar". It reads the ratio between them. That is why a drink with plenty of sugar can still taste sharp if there is a lot of juice in it, and why a pitcher that tastes perfect can turn sour after you top it up with water and ice melts into it.
Water matters too, because it sets how strong everything is. Double the water and both the acid and the sugar are halved, but the ratio stays put. That is useful: you can fix "too strong" with water and "too sharp" only with sugar.
Drag the dot on the pad. Right means sweeter, up means more lemon juice. Set the size of your jug and read off the amounts.
A classic starting point is one part lemon juice, one part sugar syrup made from equal parts sugar and water, and four to five parts cold water. In the pad that lands on roughly 14% juice and 8 to 9 g of sugar per 100 ml, right in the balanced zone. It works because the juice supplies enough acid to taste of lemon, and the sugar brings the sourness down to a level most people enjoy.
Break the rule when the fruit changes. Lemons vary in sourness from one batch to the next, and limes or a lemon-lime mix will shift the balance too. Taste a spoonful, nudge the dot, and write down what you liked.
Fix "too strong" with water and "too sharp" with sugar. They are different problems.
Dissolve the sugar first. Warm tap water works, or make a syrup with equal weights of sugar and water and keep it in the fridge. Juice the lemons just before serving, because the bright aroma fades fast. Strain out the pips; some people like pulp, and that is a matter of taste. A little zest rubbed into the sugar before dissolving it adds a lemon-oil aroma that juice alone does not have. Always chill it well, and remember that ice will dilute the jug as it melts, so make it slightly stronger than you want to drink.
For a sparkling version, mix the concentrate (juice, sugar and just enough water to dissolve it) and top each glass with chilled soda water. Cold carbonation lifts the aroma and makes the drink feel drier, so you can go a touch sweeter. Swap half the lemon for lime, add mint or a slice of cucumber, or replace some of the water with cold black or green tea for an iced-tea lemonade. Tea contains caffeine, so keep that in mind for children and for late evenings.
Lemonade is acidic, and frequent sipping over a long time can wear tooth enamel. Drink it with meals rather than all day, and rinse with water afterwards.
You need very little kit. Use fresh lemons that feel heavy for their size, since they hold more juice. A hand reamer or squeezer that catches the pips is enough. A jug marked in millilitres makes the pad's numbers easy to follow. A kitchen scale helps if you want to weigh the sugar, but a level tablespoon holds roughly 12 to 15 g.