There is no doubt at all that the PP "for him" is licensed by the head "luckily", and thus must be a complement.
Is "is licensed by" different from "is allowed by" or "is permitted by"? A lot of verbs allow/permit/license PP adjuncts/modifiers within VPs. We can say "He wept," and we can say "He wept under the bridge." Yet the PP "under the bridge" is a modifier, or adjunct, not a complement. "Put," on the other hand, requires a PP in addition to the direct object. We can say "He put the dishes in the cupboard"; however, if someone says,
*[strike]He put the dishes[/strike], one knows instantly that the speaker is nonnative. The PP is obligatory, and that, it seems to me, is why it's called a complement. Traditionally speaking, it completes the meaning.
(
Note: As I said all that, it became clear to me that I'm unclear on how "He put the dishes
away" fits into that story. Maybe "away" is an intransitive PP.)
So, I don't see why PP "for him" must be deemed a complement in "luckily for him" and "fortunately for him." The PP is permitted/allowed, and for me that means it's "licensed" -- unless that term is more loaded than I thought it was from the standpoint of linguistic jargon. In the usage I'm accustomed to, we can say that auxiliary verbs
license verb-phrase ellipsis. That means that verb-phrase ellipsis is possible/permitted/allowed after auxiliary verbs, not that it's required! We can say "I thought she was walking down the street, and she was" (VPE), but we can also say, redundantly, "I thought she was walking down the street, and she was walking down the street."
Why is "for him" a complement in "luckily/fortunately for him" if we can have perfectly grammatical sentences like "Luckily/Fortunately, he was rescued just in time"? The only thing I can think of that might tempt one to analyze the PP "for him" as a complement there is that the head of the PP, namely "for," could perhaps be said to be "selected" (another jargon term) by the adverb "luckily"/"fortunately" (heading the AdvP). In other words, while we can have "Luckily/Fortunately for him, he was rescued just in time", we can't have
*[strike]
Luckily/Fortunately on the sofa, he was rescued just in time[/strike].
Is that the hidden reason for insisting that the PP is a complement rather than a modifier?