Multi-worlds is not really relevant here. You are just asking the question how the building blocks of life form in the Universe and how can they reach a planet like ours.
But I don't think we are "lucky", because we are part of the world, not something that was placed inside it by choice. It is like asking why is Nile in Egypt and not in some other place. If Nile is in some other place, it would not be Nile...So does it make sense to say that Nile is lucky to be in Egypt? No, I think it does not make sense...
I won't comment further unless you offer a convincing proof of your assertion.
If this is the question, I think the Multi Worlds Interpretation provides the answer. Because it says that there is some worlds where any given random event will manifest.
So it follows that there is some worlds, where this random event that we call the "origin of life" manifested. And it is just that we are part of one such world.
>multiworld interpretation is one of several interpretations of quantum mechanics of the exact same evidence
I think we might think the other way around. That the origin of life, as well as the fact that we seem to be alone in the universe, as a proof of the MWI..
About the latter, I think we have an overwhelming chance to be alone, because while it is true that there can be universes where random events have lead to origin of life in multiple places, the universes where there is only a single "origin of life" event will vastly outnumber such universes that the chances of us finding oursleves in one such universe (where life has originated independently more than once) is vanishingly small.