You should really not share /var/lib/docker with multiple virtual machines. It is not just “image cache”, it is the entire Docker Data root and it could cuase issues. You would have all your metadata on all machines including existing containers and you would not have those containers running on your machne.
I don1t know if this is the cause of your issue, but each machine should have its own docker data root not used by anyone else.
You can run a locl docker registry somewhere in your environment if you want to speed up pulling images.