Hmmm, a good way to do this is to use shortcodes but I deactivated shortcodes for lay theme for now.
You can also use javascript:
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Date
You could create a textelement in the footer, give it a class and then use the "newpageshown" event to add the date string into that element.
http://laytheme.com/documentation.html#newpage-events