Georgia, not a lemon drop drinker but I can give a few hints on this and in the end you will need to practice (MJ loves this part of my 'tending) and adjust to what you like.

Measure as you go, the only way you can make consistent drinks is to get the measurements down of what you like. The wing it and pour method is stylish but not for finer cocktails.

#1, use fresh ice in the shaker, cubes. Will not be fresh if not fresh ice.
#2, I would start with about 3 oz of fresh lemon juice. Might want to add a small amount of lime juice in that three oz.
#3, Add about 2 oz of Vodka, premium vodka makes a difference.
#4, You can use Cointreau (about an oz) or in my case I would use my home made triple sec.

#5, a bit of fine sugar or simple syrup, this will be an adjust to taste item.

Now, shake that shaker until you feel and hear the ice break down and the shaker becomes cold. Strain into a martini style glass (sugar on rim if you want it) and garnish with what ever makes you happy.
This is how I would start and then go from there.

There are other orange type flavors or bitters you could add to change it up but not sure what to suggest.

I may just have to spend an evening working on these,
Todd