The only thing that comes to my mind and which is pretty easy to implement is to get rid of Related Lists default component on Lightning Page and to add every desired related list in a form of Related List - Single. That way you can keep related lists defined for Page Layout and use whatever related list you want on your Lightning Page.
Assuming you're on lightning:
You have the ability to create Lightning record pages which allows you to specify assignments based on the following combination:
Unfortunately, this only helps you with the things that the Lightning record pages control which is the UI of the page, components on page, page template, etc.