yeah, I've seen this two, and it's a bit confusing. But it makes sense, and I'm not sure how easy it is to change;
It's important to get the right names for things, as this makes it easier to understand. I'll reference the second gif, as this shows what is happeneing.
a) you have a menu, which in turn has sub-menus. You can also have submenus on that if you like. when a user navigates the menu, they go from the root menu, to the Lookups sub menu, (and potenitally more menus) until the Condition browse.
It's important to know there are only 2 pages in play here. the IndexPage with the menu, and the ConditionBrowse. The fact that you navigate through the menu is not the same as navigating through pages.
what you're really wanting is the ability to come back to the Indexpage, but have the page pre-navigate to the Lookup menu (and, BTW, still have the "back" button take you back to the main menu). That sounds to me like it's gonna be very tricky to do.
Like I say, I'm not sure this is even possible, and if it is probably isn't at the top of the list right now.
Cheers
Bruce