There's no documentation on a production installation, as far as I know. You have a couple of options:
1. There is a Dockerfile in the repo, as well as a docker-compose setup. I've deployed the LTI in a production-ish setting for evaluation purposes here at SFU using docker-compose. The only real changes I made were to use volumes on the database and fakes3 containers so they persist, and change the RAILS_ENV to production.
2. The LTI is a pretty standard Rails application, so you can stand it up using the same basic architecture as Canvas itself or any other rails app – Apache or NGINX and Passenger for the application server, a process running the jobs worker, a Postgres database server, and a Redis server. If you're already running open-source Canvas then you likely have experience setting up this kind of stack.
One warning: the LTI does depend on Amazon S3 for storing generated attendance reports. Instructure includes a
fake S3 server in the docker-compose setup. My understanding is that the links to the generated CSVs expire after 24 hours, though I haven't verified if the files are actually deleted from the bucket after they expire. If you don't have access to or aren't willing to pay for S3, and since the data is supposed to be ephemeral, you
could run the fakes3 server in a production environment, or you could stand up a S3 API-compatible service on your own infrastructure and point at that.
I haven't decided which route we're going to take if and when we decide to deploy the LTI to production.
Hope that helps.