Hi,
You’d probably need either a plugin or some custom coding to extend the menu to do so, I don’t know of any plugins off the top of my head that does anything like this though I’m afraid.
There are a few things to take into consideration if you do wish to make this your self though; Is the gallery always on the same page as the same page as the menu, if it is it’ll just be a quick JavaScript line. If it isn’t, you need to load in the gallery to every page (also a JavaScript job though) which might add frustrating delays before the images show up.
Personally I don’t think that a gallery trigger belongs in a navigational menu, it’s just not where people would expect one to be, so I’d aim to just have a link to the gallery in the menu and then let people navigate the non-lightbox version before they click through to an image they find of interest.