If I add the Zombie Lord template to a level 4 Human fighter is the final creature CR 5 or 6?
Zombie lord adds 2 racial hit die and if I am reading it correct that negates the -1 CR generally given to NPC's who normally have no racial hit die and get them only from class levels.
Your assessment doesn't include ", plus the normal CR increase for class levels (if any)." But I'm not sure what that would be actually. The CR for an NPC with only class levels is total levels - 1 right? Does that mean you add 3 and end up with CR 5? It's definitely confusing.
Look at the "sample" Zombie Lord. She is a level 3 monk. Only 1 level behind your Fighter. Her CR is 3. So class level. I would say your Fighter is CR 4.