I assume the different spellings of .simplelightbox and .simple-lightbox are typos in your question and both are correct in your code.
My first thought would be to find the function in the plugin that is fired when the white ‘X’ is clicked (that closes the lightbox) and add your line of code. If you don’t want to edit the plugin (which would have to be done every time the plugin is updated by the vendor), I would focus on the class of the white ‘X’ itself. Inspecting your page, it seems to be .sl-close. Well, you say that didn’t work.
Have you tried playing with the jQuery toggle() function? It alternates between hide() and show() depending on the state of the element.
The last thing I might suggest is seeing if you can reduce the size of the lightbox by about 5%, making it so it doesn’t overlap with your menu in the first place.