The following instructions are for the Full version of Local Map Overhaul.

Adding Local Map icons to any Item, Activator, Container, or Projectile is as simple as adding the LocalMapIcon Keyword to the appropriate form. I've included an example Keyword .ini adding icons to Nuka Cola Quantum bottles under misc files. See the KEYWORDs mod page for detailed instructions on the different ways you can manage Keywords.

Icons will be automatically assigned based on the ySI - Sorting Icons framework.
Every inventory item will already have assigned ySI - Sorting Icons textures, but Activators, Containers, and Projectiles will not. 

You can assign icons to any game form using the same .JSON framework that ySI - Sorting Icons uses for items. Check the Local Map Overhaul installation directory for an example Activator.json, where I have assigned icons to the forms supported by default. 

Here is an in depth guide on the ySI .JSON framework, the information provided can be applied to any form type, not just items.