Dunno about lag but the box system is definitely clunkier than in XY or ORAS. That was noticeable when I first tried Sun and Moon and then realized how smooth XY's is when I went back to play it briefly after.
Double battles are so laggy, I can see why they got rid of triple battles for this gen. Otherwise my 3DS has been fine for the most part, just random lags here and there. I use a regular sized New Nintendo 3DS.
I'm currently playing on a classic 3DS XL... and I haven't found any problems against lag...
Hell, even the Z-Moves are normal, there is absolutely no lag.