to swallow, to gulp something all the way down the throat
This is a rare verb for taking something down the throat. It sits beside the noun for the throat itself (לֹעַ), the part of the body that does the gulping, and beside a verb for wolfing food down (לָעַט). The family is concrete and physical: mouth, throat, and what goes through them.
Its one clear appearance comes in Obadiah, where the nations are handed the cup of God's judgment and made to drink it. The line pairs the word with drinking, so the picture is of draining a cup to the bottom: they drink, and they gulp it down. That pairing is the main reason scholars are confident about the sense here.
Hebrew has a far commoner word for swallowing something up (בָּלַע), used when the ground swallows rebels or when an enemy devours a nation. The rare word here is narrower and more bodily. It is the throat doing its work, not the idea of destroying something by consuming it.