Th' applause of list'ning senates to command, The threats of pain and ruin to despise, To scatter plenty o'er a smiling land, And read their hist'ry in a nation's eyes,
Their lot forbade: […]
We've been going through the poem one stanza at a time, but things get a bit too wacky here, and here's why: notice how Stanza 16 ends with a comma, and not a period? Yeah, we did, too. The sentence actually carries over between stanzas! This is called enjambment, and it can trip you up if you're not careful.
Okay, so if we unravel the weird sentence structure, we can figure out what's going on here. You actually have to start at the end: The dead villagers in the graveyard are replaced with the pronoun "Their" in line 65.
The dead villagers' situation, or "lot," kept them from receiving ("commanding") the applause and approval of politicians.
Their situation also made it impossible for them to blow off threats of pain and ruin.
Nor could they spread good stuff ("plenty") all over the country, even though that would win them a place in the history books in the eyes of their countrymen.
Nope, the villagers were poor and died unknown because of their poverty, or "penury," as the speaker calls it in Stanza 13.