"Yeet me down a bae" is a newer Lucas catchphrase, and an odd use of language. It is, at the very least, a very idiosyncratic and nonstandard use of slang associated with youth culture. The expression seems particular to Lucas, and due to his schizo speech patterns, requires a bit of translation.
Nobody but Lucas is out there going "Yeet me down a bae."
"Yeet," generally a nonsensical exclamation of surprise or enthusiasm, can also mean "to throw." "Bae" means girlfriend or boyfriend. So Lucas is saying "Throw me down a girlfriend." This requires further explanation.
The idiom of "to throw down" most commonly means: 1) to fight, 2) to eat, 3) to challenge, 4) to perform, 5) to have a party, and 6) to contribute money to. All interesting considering Lucas and the rest of the sentence ("I'm going to eat a bae," "I'm going to fight a bae"), but not what Lucas is getting at.
A less common use of "throw down," attested to by Urban Dictionary, is to "to introduce someone to, or break the ice for."
So Lucas is saying "Introduce me to a girl friend (because I am a creepy faggot)," in the most awkward, faux-youth way he can. He is addressing God, who he doesn't believe in, like some flatbill who's got the hook up.
