Well, LXD doesn't actually exist yet, so Docker couldn't possibly be built on it.
You are likely confusing LXD with the present day LXC, which is understandable. You thinking that Docker is built on LXC is also understandable - but also not quite right.
Docker used LXC as the default container implementation for much of it's lifespan. However, it has since dropped LXC as the default and uses libcontainer instead.
The linux kernel does not actually specifically have a container implementation. Userland tools such as LXC ( https://linuxcontainers.org/ ) and libcontainer ( https://github.com/docker/libcontainer ) utilize things like kernel namespaces, cgroups, and a variety of other features to deliver the container experience.
You are likely confusing LXD with the present day LXC, which is understandable. You thinking that Docker is built on LXC is also understandable - but also not quite right.
Docker used LXC as the default container implementation for much of it's lifespan. However, it has since dropped LXC as the default and uses libcontainer instead.
The linux kernel does not actually specifically have a container implementation. Userland tools such as LXC ( https://linuxcontainers.org/ ) and libcontainer ( https://github.com/docker/libcontainer ) utilize things like kernel namespaces, cgroups, and a variety of other features to deliver the container experience.