There is more

Can we concentrate on one? I feel like chasing a running target.

It is not.

You have systemLog.path set to /var/lib/mongo/mongod.log

You have pidFilePath set /var/lib/mongo/mongod.pid

In the log we see that if fails to write into /data/mongodb/lib but from the ls output we see it is writable.

Humm …

Is /data/ NFS mounted?

I would not recommend a non-local or non-SAN disk.

Does the local mongod user has the same UID as the NFS host mongod user?