Please note that Docker and LXC (and LXD by extension) are essentially the same technology packaged differently, with different yet overlapping use cases; in fact, early Docker Engine was based on LXC before they switched to containerd.
Therefore I don't think there is anything that can run on LXC/LXD but not on Docker (and vice versa); it's more a matter of preference, whether you want a long-lived persistent virtual system (LXC/LXD) or ephemeral single-application containers with optional persistence (Docker).
Still, nothing stops you from using LXC/LXD for ephemeral containers and Docker for long-lived systems, but you'd be using the non-optimal tool.
Therefore I don't think there is anything that can run on LXC/LXD but not on Docker (and vice versa); it's more a matter of preference, whether you want a long-lived persistent virtual system (LXC/LXD) or ephemeral single-application containers with optional persistence (Docker).
Still, nothing stops you from using LXC/LXD for ephemeral containers and Docker for long-lived systems, but you'd be using the non-optimal tool.