Our speaker is an insomniac. Perhaps he's lying in bed, eyes wide open, staring at the ceiling. He's listening to every little sound and his mind keeps turning. Still, we can't help but notice that the poem doesn't tell us any of this explicitly. Our speaker says nothing about what he's doing, or about his physical surroundings other than a suggestion that he's inside a house. There are bare rooms over his head. But then again, who's to say those rooms aren't metaphors?
Lacking any more information, we Shmoop sleuths have to conclude that this guy defines himself entirely through his relationships with his brother, his father, and God, which is not something we're used to. A lot of poems (and people in general) are all about me, myself, and I. This is what I see, this is what I feel, this is what I think, this is what I smell. Of course, there is some projection going on in "This Hour and What Is Dead." When the speaker talks about the restlessness of his brother, for example, it's pretty clear it's his own restlessness that he's actually talking about.
After all, this guy is a thinker, and it's his thoughts that keep him awake. He ponders what his brother is up to: "What could he possibly need there in heaven?" (5). And he makes comparisons that help him understand: "His love for me is like his sewing" (16). It's clear that his love for his brother and his father (and their love for him, for that matter) haunts him, but he's doing his best to understand why.
Still, beyond the deep respect and love he has for his pops and bro, our speaker also wants to be free from the burden of that love and those memories. We get the feeling this might be a person who was raised with a deep respect for family and God (however he thinks of God), and it's a big deal to make this plea for independence from those important things. But maybe, just maybe, those memories are too painful for our speaker. He just wants to move on with his life. Why else would he want "the Lord to leave me alone" (31)?