Haere Mai from New Zealand!
Other cultures may have similar stick games but the words you give are a phonetic transcription of Maori words, to the second verse of the following song by W. Tawhare.

E Aue! E Ka mate au!

E papa waiari taku nei mahi
Taku nei mahi he tukt roimata
E papa waiari taku nei mahi
Taku nei mahi he tukt roimata!
Chorus:
E au-e! E kamate au!
E hine hoki mai ra.
V2:
Maku e kau-te o hikoi tanga,
Maku e kau-te o hikoi tanga.


Phonetically it's sort of like this:

Ay pa-pa why are ee tar coo nay mar hee.
Tar coo nay mar hee hay too coo roy mar tar.

Ay oh ay! Ay car mar tay oh,
Ay hee nay hoe key my rah!

Mar coo ay co tay or hee coy tar na,
Mar coo ay co tay or hee coy tar na.

I don't recognise the name Lumi sticks. Here we just refer to it as a Maori stick game though the Maori name is Tititorea.
That was the one we learnt at Girl's Brigade about 40 years ago. We did it in pairs but the advanced version has 4 people sitting in a square and the sticks are thrown diagonally across the square as well as just across to your partner - without dropping them! I think the final bit had all eight sticks flying at once, around in a circle, passing the one from your left hand to your right and your right one to the person on your right, while simultaneously trying to catch the one thrown from the person on your left, in your left hand!
Got that?
But for beginners, holding them upright, just tap the bottom of the sticks on the ground, then click them together in front of you, twice, at about chest height. That's verse 1.
The next bit uses movements similar to Pat-a-cake, tap the ground, click together once, then throw the one in your right hand across to your partner's right hand, and with the same movement, catch their one. Then repeat that but throw and catch them in your left hand.
After that you get into stuff that's a bit too awkward to describe, where the sticks are flipped over end to end or swapped from hand to hand in all sorts of tricky combinations.
Give it a go. We had cut-off bits of a broomstick but it's much easier on the hands (and knees) if you use rolled up newspaper, held tight with sticky tape around the top and bottom.
Haere ra,
Robyn