In the example below, the error 0516-070 : LVM system call found an unaccountable internal error. was due to full / (slash) filesystem.
Since it was the first time I have seen this error, I do not know if it could be associated with other problems but for sure you can find yours by looking into errpt.

aix / # lsvg rootvg
0516-070 : LVM system call found an unaccountable
        internal error.

aix / # errpt
ksh: No space left on device
IDENTIFIER TIMESTAMP  T C RESOURCE_NAME  DESCRIPTION
F7FA22C9   0125144614 I O SYSJ2          UNABLE TO ALLOCATE SPACE IN FILE SYSTEM
aix / # errpt -aj F7FA22C9
ksh: No space left on device
---------------------------------------------------------------------------
LABEL:          J2_FS_FULL
IDENTIFIER:     F7FA22C9

Date/Time:       Sat Jan 25 14:46:14 2014
Sequence Number: 15
Machine Id:      00A64B804A00
Node Id:         aix
Class:           O
Type:            INFO
WPAR:            Global
Resource Name:   SYSJ2

Description
UNABLE TO ALLOCATE SPACE IN FILE SYSTEM

Probable Causes
FILE SYSTEM FULL

        Recommended Actions
        INCREASE THE SIZE OF THE ASSOCIATED FILE SYSTEM
        REMOVE UNNECESSARY DATA FROM FILE SYSTEM
        USE FUSER UTILITY TO LOCATE UNLINKED FILES STILL REFERENCED

Detail Data
JFS2 MAJOR/MINOR DEVICE NUMBER
000A 0004 
FILE SYSTEM DEVICE AND MOUNT POINT
/dev/hd4, /

Remember, you will not be able to increase / if it's full because you will get the same error. You will have to do just a bit cleaning first in order to have a successful increasing command:

aix # chfs -a size=+128M /
Filesystem size changed to 786432

Now a successful "lsvg rootvg" command:

aix # lsvg rootvg
VOLUME GROUP:       rootvg                   VG IDENTIFIER:  00c64e8000004c0000000143c6345968
VG STATE:           active                   PP SIZE:        128 megabyte(s)
VG PERMISSION:      read/write               TOTAL PPs:      1536 (196608 megabytes)
MAX LVs:            256                      FREE PPs:       1426 (182528 megabytes)
LVs:                12                       USED PPs:       110 (14080 megabytes)
OPEN LVs:           11                       QUORUM:         3 (Enabled)
TOTAL PVs:          4                        VG DESCRIPTORS: 4
STALE PVs:          0                        STALE PPs:      0
ACTIVE PVs:         4                        AUTO ON:        yes
MAX PPs per VG:     32512                                     
MAX PPs per PV:     1016                     MAX PVs:        32
LTG size (Dynamic): 512 kilobyte(s)          AUTO SYNC:      no
HOT SPARE:          no                       BB POLICY:      relocatable 
PV RESTRICTION:     none                     INFINITE RETRY: no