Does the launcher need to be open (phone unlocked) for variable changes to take effect?

I have a Tasker variable that sets the visibility of some icons. It seems that the var doesn’t change unless I run it directly from the phone, rather than having it trigger when the screen is locked. Is this a limitation, or is there another way to do this?

I’d like to create dynamic icons of contacts, that change depending on who I last called. Is this possible in LL?

Also, looking for the same with SMS