No, it sounds right. There's matcha, but with the acid from the lemonade curdling the milk, it's used to clump shit together so that the drink can be filtered and clarified. I've never tried it, but I've seen the technique used a number of times.
Yeah same concept as a milk-washed cocktail, which cuts down on the bitter/astringent flavors in liquor. Works really well, I bet this drink would be delicious
I don't know enough about the chemistry going on to give you a confident answer. I assume not though - I don't think curdling milk gets rid of all the lactose, and since you're essentially using curdled milk as a filter with this technique, I wouldn't be surprised if a non-zero amount of lactose made it's way through the filter. I'd have to do some actual research to know for sure though.