I'm pretty much done with that game but there always seems to be something else to add :) At the moment, I'm working on Undo support which should make the game a little more fair.
Consider checking out this template with touch controls for phones:
I use a modified version here:
In Chrome, if you open the dev tools, you can simulate a phone with touch controls, reload the page and see what the controls look like for different phone sizes.
Touch controls come from:
I modified the template to make the buttons fit better for this game and to add a Menu button (missing from the template).
As for lag, I just uploaded binaries for Windows, Mac, and Linux so maybe give one of those a try?