This recipe is very flexible with the herb proportions (and pretty much everything else, too). You may adjust the mint and basil to your taste. Mint tends to add a little more sweetness, and basil, a little more robustness (although still subtle). Keep the dill to a minimum. It is just a very light hint to enhance, and you don't want to really notice a distinct flavor there.
Although I have never actually tried, I would not attempt using dried herbs for this drink - USE FRESH!
If using fresh lemons, you may want to add more sugar and/or water to balance it out as some lemons can be very tart. (I don't like to go super-sweet, personally, but this is obviously a personal taste issue again.)
Dress it Down:
If dill scares you, just go ahead and eliminate it.
Substitute for all mint or all basil instead of the combo.
In a time-pinch, you may use the syrup immediately after making it (not steeping the additional time in the fridge). You may want to up the herb amounts a little bit to try to get more flavor in there.