You can make a really good lemon-lime using, no surprise, lemons and limes. However, lemons and limes vary in size and cost, they spoil, and also take a bit of work to cut and squeeze. The easier and more consistent way is to use lemon and lime oils for the flavor, and a blend of citric and malic acids for the sourness.
I've been using Boyajian oils, which you can get in a set of three, orange, lemon, and lime. They can also be used in place of citrus zest, 1/4 tsp or 24 drops per 3 tsp zest; really handy. The emulsifiers (gum Arabic and xanthan gum) in the syrup allow the oils to blend in, rather than pooling on top.
Acidity is a huge part of the flavor of citrus, and of soda. You can try only using the citric acid, but using the malic also makes this more like real citrus fruit. Malic acid is the sour in lots of super-sour candy. It's also the main acid in apples.