NLM locking issue between HP-UX 11.11 NFS client and RHEL NFS server

Issue

We previously had an HP-UX 11.11 system as an NFS server exporting a couple of directories for HP-UX 11.31 and RHEL 6 clients. The server function was moved to a new RHEL 6 system exporting to the original HP-UX 11.11 (as a client now) and the same HP-UX 11.31 and RHEL 6 systems as previously. We're having file locking issues on the HP-UX 11.11 system after this change. It can only use NFSv3. The RHEL and HP-UX 11.31 systems are all using NFSv4. We're seeing errors such as this:

ERROR:   Cannot lock some/file at
         "/path/to/some/file" due to fcntl()
         error "ENOLCK".  If the soc is on a remote NFS file system,
         the NFS locking facility is probably inactive or having
         problems.  If it is on a local file system, this indicates too
         many locks are already in use and no more are available.

ERROR:   Cannot read the target
         "/path/to/some/file".

And:

> inctl -i lock.test
Tue 09:48:18 AM CDT inctl: cannot test lock lock.test 46 : No locks available