Hi Ragesh,
There are three ways to achieve what you want:
1. Clear the root file system by deleting unwanted files.
a) du -kx | sort -rn | head -20
Now look for file you don't require and delete or move them.
Also, keep a track of yout root files sys growth size....it should not growing heavily.
2. Add another disk to Vg00 and do a pvmove of lvol4 and the extend lvol3 because lvol1,2,3 needs to be contiguous (a hectic and time taking method).
#/usr/sbin/pvmove -n lvol4_path source_pv_path dest_pv_path (you do this only for lvol4 or even for lvol5 depends on space requirement)
Extend the root LV.
#lvextend -L 4000 /dev/vg00/lvol3
#fsadm -b 4000M /
For illustrative examples on this have a look on this link.
http://www.symmetricwebsites.com/articles/HP-UX/hpuxDynamicallyExtendSlashAndOrStand.php3. Take ignite backup of VG00 and restore it, while restoring you can change the root fs size. This would be easy I suppose. But if you are going with this, take at least two good ignite backups. While booting from tape you can select "interactive" snd "advance" optons to set file sizes.
Hope this help !!
Regds..
Don't fix what ain't broke