"Lui" is the indirect object of "il" That said, let's look at the two sentences you cite (and I am taking the liberty of abbreviating them a bit):
1) Il lui manque une oreille -- He is missing an ear. Literally this would be translated as: "It is an ear missing from him". The "from him" is the indirect object, hence "lui".
2) Il lui arrive de nous faire un cadeau. -- He happens to make us a present. Literally: It happened to him to make us a gift. Again the "to him" is the indirect object, i.e., "lui" in French.
Yes, "lui" could also be the stress pronoun but not in these cases. Stress pronouns usually are at the end of sentences or following prepositions. Neither is the case here.
I suggest you check out the lessons on indirect objects.
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