I've just managed to set up Listmonk on Unraid. I haven't made a template because my process was slightly more-involved than that, but I've documented the whole thing in a blog post at https://danq.me/listmonk-on-unraid. I hope that'll help somebody else!
The short version is that you'll need
a separate Postgres installation
to make Listmonk's config.toml (pointing to that Postgres installation) and mount it into the Listmonk image as a path
to start the container... it'll immediately stop itself
run, from a shell on your Unraid box, something like this to spin up another copy of Listmonk (temporarily) to do the DB setup:
docker run --rm -ti --net='host' -e TZ="UTC" -v '/mnt/user/listmonk/config.toml':'/listmonk/config.toml':'rw' listmonk/listmonk:latest ./listmonk --install
to start the container again: now it should work!