Topic starter don’t use docker containers. He use lxc containers. LXC is virtual machines on host kernel. Case is that: He have 3 virtual machines with shared disk. In 3 VMs have 3 different applications. Applications work under different users and can’t rewrite data on shared disk. That is user permissions problem.
I used lvm with SSD cache few years, but time to time I have problems with loads after reboot. If forgot about reboots all work great with LVM raid + LVM cache. Cache can be configured without raid. And you can add or remove cache in any time. Docs: https://man.archlinux.org/man/lvmcache.7