Eu resolvi isso consultando o link . Eu só preciso estender o volume lógico e estender o sistema de arquivos.
twadmin@analysis-db:~$ sudo lvextend -l +100%FREE /dev/analysis-db/root
Extending logical volume root to 59.26 GiB
Logical volume root successfully resized
twadmin@analysis-db:~$ sudo resize2fs /dev/mapper/analysis--db-root
resize2fs 1.41.14 (22-Dec-2010)
Filesystem at /dev/mapper/analysis--db-root is mounted on /; on-line resizing required
old desc_blocks = 2, new_desc_blocks = 4
Performing an on-line resize of /dev/mapper/analysis--db-root to 15535104 (4k) blocks.
The filesystem on /dev/mapper/analysis--db-root is now 15535104 blocks long.
twadmin@analysis-db:~$ df -h
Filesystem Size Used Avail Use% Mounted on
/dev/mapper/analysis--db-root
59G 25G 31G 45% /
udev 2.0G 4.0K 2.0G 1% /dev
tmpfs 793M 228K 793M 1% /run
none 5.0M 0 5.0M 0% /run/lock
none 2.0G 0 2.0G 0% /run/shm
/dev/sda1 228M 45M 171M 21% /boot