[root@linux Tivoli]# df -h .
Filesystem            Size  Used Avail Use% Mounted on
/dev/mapper/rootvg-tivolivol
                      279M  237M   29M  90% /opt/Tivoli

Increase first the size of logical volume:

[root@linux Tivoli]# lvresize -L+128M /dev/mapper/rootvg-tivolivol
  Extending logical volume tivolivol to 416.00 MB
  Logical volume tivolivol successfully resized

Resize online the filesystem according to lv size:

[root@linux Tivoli]# resize2fs /dev/mapper/rootvg-tivolivol
resize2fs 1.39 (29-May-2006)
Filesystem at /dev/mapper/rootvg-tivolivol is mounted on /opt/Tivoli; on-line resizing required
Performing an on-line resize of /dev/mapper/rootvg-tivolivol to 425984 (1k) blocks.
The filesystem on /dev/mapper/rootvg-tivolivol is now 425984 blocks long.

Filesystem resized:

[root@linux Tivoli]# df -h .
Filesystem            Size  Used Avail Use% Mounted on
/dev/mapper/rootvg-tivolivol
                      403M  237M  146M  62% /opt/Tivoli