What will happen if I add lemon juice with my milk in my cupcake?

Use both the zest and the juice, steer away from the extracts though as they tend to have a soapy flavour. Don't worry about the milk curdling, it just becomes buttermilk, which many cakes call for in the first place.

As others have said, you can add lemon zest to the batter to get lemon flavor into the cake part. If you are frosting the cupcakes, you can intensify the flavor there, depending on your recipe. I would look for a lemon buttercream recipe, or you can use a tart lemon glaze of sugar and lemon juice drizzled over the cake.

Use limes! They have a more intense flavor so you can get more of that flavor than using lemons.

King Arthur Flour also has this amazing product called powdered lemon juice. It is concentrated lemon juice in solid form. Great to add lemon flavor to any baked goods withou curdling milk or adding extra liquid

I agree that you should use lemon zest and lemon extract instead of juice. The pH of lemon juice will change the consistency of the finished product (says the person who has tried this…..).

If you want to add lemon flavor to a cake recipe that doesn't have it in the original, I would use lemon zest and/or lemon extract. Lemon juice will not add enough flavor on its own, and will cause your milk to curdle.

Lemon juice will cause the milk to curdle, which means you might need to use baking soda in place of baking powder. I think using lemon zest will give you a better result.