According to the Merriam-Webster dictionary, one of the meanings of "to lay off" is :
to lay off : to leave undisturbed.
How would this definition fit within the context "to lay off of him" for example ?
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I think the context you are referring to means to leave someone alone or to stop bothering or even stop hurting/attacking someone.
Person 1: "It's Person 2's fault!"
Person 3: "Hey, lay off him!"
"Lay off of someone" is just an idiomatic variation. It sounds more like AmEng than BrEng to me and in my opinion not grammatically correct (or at the very least is a tautology), but from my experience of US culture, it is commonly spoken.
In a very different context "lay-off" can also mean to terminate someone's employment, although this would normally be phrased "lay someone off".