Migrating existing Lumen application from Homestead to Docker?

I've written an application in Lumen which runs on Homestead. I found that after I wrote it that our server doesn't support the version of PHP that Lumen/Homstead requires.

Having had luck with Docker in the past, I'd like to use it to work around this problem. However, I'm having trouble finding a clear and complete tutorial on how to get my existing Lumen application to run on Docker. Does anyone know how to do this?

Cheers, Bret