I think in discussions its useful to deal with defaults because there are always workarounds. For Docker the default is to run init less containers so you do not get a normal OS environment. For LXC the default is run init in the container so you get a container with a normal OS environment out of the box, more like a VM.
lxc-start by default will start the container's init and any apps installed with services will start with container start. lxc-start has no options or documentation I have seen that enables users to launch as a single process without starting the container init so it will be useful to share how that works.
With Docker you launch the app in the container directly from the host and if the app is a daemon for instance Nginx, you need to disable daemon mode or it won't work as there is no init process to manage background processes. So with Nginx you would need to disable daemon mode in nginx.conf or start it with 'nginx -g "Daemon off"' in Docker. In contrast with LXC you install Nginx and it will work as it would on bare metal or VMs. There is no need to think about how the app manages its processes
To run multiple processes or daemons in Docker you need to use a shell script, or use a third party process manager like supervisord for instance. The entire Docker ecosystem, and tooling is built and defined around single process containers.
A ton of problems around deployments especially for multi process apps, daemons, databases or any apps that require cron, logging, agents etc emanate here. This becomes a process in itself to know how the apps operates and then to configure it accordingly. Your deployments also become docker specific, for instance Nginx with a Wordpress stack deployed on bare metal or VM can move seamlessly to an LXC container and vice versa because they all run normal OS environments.
This can't happen with Docker and you need to re-engineer deployments. Why take on this extra load, and create incompatibility from a non standard OS environment, or worse give up the init that comes for free for for a third party process manager to do the exact same thing, only with more effort and cognitive load? This doesn't make much sense unless there is an extremely clear upside and use case.