The Odyssey (whole poem): As far as source material goes, it's pretty tough to get much older, more famous, or more important than Homer's Odyssey. This epic poem, written more than 2000 years ago, has had a major impact on Western literature. In "The Lotos-Eaters" Tennyson is riffing on a particular moment in Book 9 of the Odyssey, when Odysseus and his men get blown off course and find themselves in the land of the Lotos-eaters. Several of the guys fall under the spell of the place, and refuse to leave. Finally, Odysseus has to tie them up and drag them back to the ship in order to get things moving again.
The Trojan War (whole poem): Odysseus' famous voyage takes place on the way home from the Trojan war, so it makes sense that the war comes up in this poem, too. You can read up on the legend of that big ruckus here. Basically, like a lot of episodes in Greek mythology, it started with a fight between the gods that whipped up the mortals, too. Whether or not it was an actual historical event is still up for debate, but it certainly gave us some great stories.