I hope i can help you at least in the right direction :)
The Menu is always there, its just hiding, however it is hidden out of the view of the user ( to the right of the viewport/browser window )
When you hover over the Menu items, A class gets added to the opening <html>. The class 'visible---nav'
( Note: you could also add the class to the opening <body> tag ):
When this class gets added, along with it comes some new CSS to be applied to the Menu - " transform:translateX() "
This forces it Left across the screen and into view. The smooth slide is achieved through a CSS 'transition'
You would be able to achieve this by adding Custom Code within 'Lay-Options - Custom CSS & HTML'
Some links to help:
On Hover - AddClass ( the CSS way ):
On Hover - AddClass ( the JS way ):
You will need some basic knowledge of CSS or JS to achieve this, here on the Lay Theme Website we have some help on the subject:
Here is a link to a thread with a similar subject:
I hope this helps & have a wonderful day! :)