A few years ago, while attending a GIML Professional Development Level Workshop (PDLC), we were tasked with composing a song in Lydian tonality. Always up for a challenge, I tried my hand at writing a round in this unfamiliar tonality. It turned out to be pretty good!
I finally got around to making a video of me performing all 3 parts. Here it is (including a surprise visit from my nosey cat, Edie):
You can see the notation in this Sibelius-generated video I made a while back:
It is available both in my PDF book, Modal Rounds for Choir and in my book Fifty Tunes for Teaching.

Fifty Tunes for Teaching
Check out this book which contains 50 new songs with and without words for use in the general music class. Sequenced according to Gordon's Music Learning Theory.