I think the way Gigalixir works (and also Heroku, Render.com etc) is that they provide you the SSL layer for you, and in your own application you should only be concerned with HTTP layer, and maybe a redirect from HTTP to HTTPS.
So you set up your application the usual way, with listening only over HTTP on $PORT, then add custom domains in Gigalixir and set up redirect - all without changing anything in your code, but rather by altering the Gigalixir configuration with it’s CLI:
https://gigalixir.readthedocs.io/en/latest/domain.html#how-to-set-up-ssl-tls
