The speaker of "On My First Son" imagines family as a kind of financial arrangement. God or Heaven lends the speaker his son for a time (in this case, just seven years). After that time has expired, the speaker has to pay back the child, so to speak. While it is kind of weird to think of family in this way, the speaker is at least able to offer some explanation for his son's death.
Line 3: The speaker says his son was "lent" to him for seven years. "Lent" is here a metaphor to describe the son's short life on earth. The speaker also says he has to "pay" back his son. The use of the verb "pay" carries forward the metaphor by likening the son's death to repaying a loan.
Line 4: The son's death is "exacted" from the speaker. "Exacted" is another metaphor to describe how God or Heaven takes the son back from the speaker.
The speaker is writing about the death of his first-born child so, naturally, he's upset. But he doesn't just talk about his feelings with respect to his child. This guy feels all the feelings, and he goes on to claim that the world is full of things that cause "misery," pain, and sadness. In fact, in the end he thinks that sometimes death can be a good thing, since one gets to escape from all that nasty, sorrowful stuff (aging, disappointment, etc.).
Line 5: The speaker wishes to abandon all thoughts of fatherhood because the very thought of being a father now makes him sad.
Line 6: The speaker suggests that one shouldn't "lament," or feel sadness about, death.
Lines 7: Why not? It's because death allows us an escape from the pains of the world and of the flesh—things that might cause pain and sadness. He calls this "flesh's rage," which is a personification of inanimate body parts, giving them human emotion.
Line 8: Death also allows us to escape from old age, which the speaker considers a "misery."