This may be too late - you might have wanted this for the 4th but . . .
I have never made vodka mint lemonade but I have made mojitos for a crowd (gallons of it for a party), which is relatively similar.
I made a large batch of mint simple syrup (can be done many days ahead of time). I don't like my mint in the hot sugar water, I think it can make it taste a little skunk-y (though not as bad as other herbs). So I make the simple syrup (1:1) and then put some of the room temp syrup in a blender with a ton of mint and blend. Then strain to remove mint bits.
I then mix this with lemon juice and vodka - float some mint in it for looks - and voila. The lemon juice is the tricky part (for the mojitos I needed lime juice). I'd stay far away from the pre-squeezed, shelf stable bottles in the grocery isles. It doesn't taste right. I actually went to the fruit counter at my Whole Foods which uses a commercially squeezed fresh juice in their cut fruit preparations. They sold me it by the bottle for what I thought was very reasonable price (can't remember how much). It was the closest I could get without spending days squeezing fresh limes. Though I have since done it for a more casual gathering and used a mixture of lime-aide, weaker simple syrup (since lime-aide already has a lot of sugar) and a bottle of key lime juice to bring back some tartness.
I put the finished cocktail in one of those big glass beverage containers with the spout on the bottom. It was a huge hit and we went through a little over 6 gallons of it.