Recipes that specify fresh lemon or lime are being specific for a reason. The acidity can be replaced easily; the aroma cannot, and the two are usually confused.
Juice loses its top notes within hours
The bright aromatic compounds in citrus juice are volatile and begin escaping as soon as the fruit is cut.
Within a few hours the juice tastes flatter, and within a day it develops a stewed character that is obvious alongside a fresh sample.
Lime deteriorates fastest, which is why bars that pre-juice at all will juice lemon in advance and lime as close to service as they can manage.
Pasteurisation changes bottled juice permanently
Shelf-stable juice is heated to prevent spoilage, and that heating drives off volatiles and creates cooked notes that were not in the fruit.
Preservatives added for stability contribute their own faint character, which is noticeable in a drink where the citrus is the dominant flavour.
Bottled juice is therefore useful where citrus is a background acid and poor where it is the point of the drink.
The acids themselves differ between fruits
Lemon juice is dominated by citric acid, while lime carries citric acid alongside a higher proportion of other acids and a different sugar content.
The two are close enough in strength to substitute by volume and different enough in character that the resulting drink is not the same recipe.
Grapefruit is considerably less acidic and much more bitter, so it cannot be swapped in without adjusting the sweetening as well.
Oil from the peel is part of the ingredient
Hand-squeezing and mechanical presses both express a small amount of peel oil into the juice, and that oil carries much of the perceived freshness.
Juice extracted without any peel contact tastes noticeably duller, which is part of why some commercial juices seem thin even when fresh.
This is also why a garnish of expressed peel partly compensates for older juice, restoring the aroma if not the taste.
Acid solutions solve a different problem
Citric and malic acid dissolved in water reproduce the sourness of citrus precisely and keep indefinitely, which suits batching and large-format service.
They carry no aroma at all, so they are used alongside a small quantity of fresh juice or an oil-based aromatic rather than instead of them.
Used as a straight replacement, they produce a drink that is technically balanced and reads as strangely empty, which is the clearest demonstration that acidity and aroma were doing separate jobs.