A lot of times this happens.
I wonder why you call it “running late“? What’s its etymology? I looked up a superficial explanation initially and ran into several brick walls. All explanations and a book (which I’ll read) except the targeted one. But, an etymological definition of “run” has provided a little understanding. Perhaps.
“Run” can also mean “to maintain” or “keep going”, etc. So, conclusion: “running late” is “late is late”.