I couldn't load the game but I suggest you to try to search about doing a layer with a parralax of (0, 0), this should eradicate lag (I think the manual precise that anchor behavior is meant to be used on layer with (0,0) parralax)
Edit: I see it now, DOM Elements (button and textbox) are not actually drawn by C2 inside the canvas, they are on top, and so I do not think moving them in a non laggy way is doable, could be wrong though.