Is your server a dedicated server, or a VPS? Because if it's a VPS, you're probably already running in a VM.
Adding a VM might provide more security, especially if you aren't an expert in LXC security configuration. It will add overhead. Running Docker inside Docker provides nothing but more overhead and unnecessary complexity to your setup.
Also, because it isn't clear to me from your post: LXC and Docker are two ways of doing the same thing, using the same Kernel capabilities. Docker was, in fact, written in top of LXC. The only real difference is the container format. Saying "running Docker on LXC" is like saying "running Docker on Docker," or "running Docker on Podman," or "running LXC on Docker". All you're doing is nesting container implementations. As opposed to VMs, which do not just use Linux namespace capabilities, and which emulate an entirely different computer.
LXC, Podman, and Docker use the underlying OS kernel and resources. VMs create new, virtual hardware (necessarily sharing the same hardware architecture, but nothing else from the host) and run their own kernels.
Saying "Docker VM" is therefore confusing. Containers - LXC, Podman, or Docker - don't create VMs. They partition and segregate off resources from the host, but they do not provide a virtual machine. You can not run OpenBSD in a Docker container on Linux; you can run OpenBSD in a VM on Linux.