I'm not quite sure how this popup works from your side, but from here, it looks like this, displaying the MOBILE MENU ... and correctly so, because the popup window is only 960px, which is below the "breakpoint" which triggers the mobile menu:
Thus, even before diagnosing this issue, I can't see that anyone will even see the topbar menu, unless they specifically resize the popup window. Why even use a popup window in the first place? I find it annoying, and will often just copy the link, and instead open it in a new tab.
Apart from the above, it seems you are right that the carousel images don't appear AFTER resizing the window up so the topbar appears. I know WHY this is happening: Because at the point of load, the carousel images "don't exist", thus the lazy-loader will not load them. I will look into this ...
However, logically speaking, surely you would not want the visitor to have to resize the popup window to view the topbar menu? If I resize the popup window UP so that the topbar menu will display, and then refresh the page, the menu works as expected:
If you really want to open the website in a popup window AND be sure that the topbar menu displays, then set the popup window to width 1024px or higher. If you don't set it to 1024px+, nobody will really see the topbar menu anyway, unless they resize the browser, which would be a counter-productive process to expect.