In American English the term
refers to the drink made with lemon juice (fresh squeezed preferred), flat water and lots of sugar, no alcohol at all, and no carbonation. If it is colored pink (with some red juice or coloring), you'd call it 'pink lemonade', which is not uncommon. A lemonade drink colored to the point of being red is unknown.
In AmE, if you have a lemon drink that is carbonated, you wouldn't have a word for it, except maybe by borrowing like the foreign brands 'Limonata'. If any carbonation is involved, the word lemonade would not be either.
A lemon flavored drink made with alcohol (and possibly carbonated water) is known as
based on the the term to differentiate alcoholic from non-alcoholic apple drink, 'hard cider' and 'apple cider' (the latter being non-alcoholic in general AmE).