How to map LAN network share to Docker volume?

Nope. Every volume must be configured from the perspective and needs of a particular container.

You can find the UID and GID required by a container by running these commands:

# find user name that runs the main process in the output
docker exec -u 0 {container id or name } ps
# find uid/gid of the user 
docker exec -u 0 {container id or name } id {USER}