Another idea: Make a tincture/ cold infusion.
Wash and dry your lemons and mint. Dice and freeze the lemons; freeze the sprigs whole in a bag. Beat the bag about a bit to detach the leaves. Place frozen lemon chunks and frozen leaves in blender. Whiz to powder. To make a cold infusion, add water; to make a tincture, add vodka (well, not really a ...
Thank you to rumtscho for helping me to improve this answer in terms of clarifying its relevance to the question, partly by expanding upon the other respondents' reasons for having suggesting alternative strategies (freezing rather than refrigerating; not combining reactive ingredients).
The answer to your question as posed (storing the two ingredients, ...
I would like to add that you can just freeze the mint leaves without grinding them too. Wash and dry them well, then... Put them in the freezer. If they're fresh and dry, then they won't stick together, and you can pull out as many as you like at a time.
That said, if you let the leaves thaw, they'll look and feel like they've been blanched. The water in the ...
I've had experiences in the past where herbs + lemon juice ended up getting a kind of "pickled" taste because of the acidity of the lemon. I might just grind the mint and freeze that on its own, and freeze lemon on its own, without combining the two.
I'd make it into ice cubes.
They'd add decorative interest too.
Fridge, maybe a week, freezer, more like 6 months.
There's a full list of storage times in How long can I store a food in the pantry, refrigerator, or freezer?