Try flock command:
exec 200>"$LOCK_FILE"
flock -e -n 200 || exit 1
It will exit if the lock file is locked. It is atomic and it will work over recent version of NFS.
I did a test. I have created a counter file with 0 in it and executed the following in a loop on two servers simultaneously 500 times:
#!/bin/bash
exec 200>/nfs/mount/testlock
flock -e 200
NO=`cat /nfs/mount/counter`
echo "$NO"
let NO=NO+1
echo "$NO" > /nfs/mount/counter
One node was fighting with the other for the lock. When both runs finished the file content was 1000. I have tried multiple times and it always works!
Note: NFS client is RHEL 5.2 and server used is NetApp.