I used to run before like early in the morning and then lift/grapple later the evening. I did that because I felt my running felt better fresh and it didn't seem to take away anything from the two other.
This is just how I think of it: If you run before you're a bit more tired which forces you to use better technique. The same if you lift right before training.
Would it be better to run immediately before or immediately after training?
When I say training I mean grappling for 1.5 hrs btw