This lat sep in procedural towers is not an invention - it's obviously just something you can't come to grips with.
They are on different routes - 180° apart. In fact, they are further apart than two aircraft on tracks that vary by 80° - or can't you work that out either.
I suggest you go and talk to a controller - in fact better talk to a few of them as you won't believe just one - who has worked a procedural tower and ask him/her whether my example is laterally separated or not. I await your answer.
Still working after 30 years and by the looks of it forgotten more than you'll ever know.