At first, we were getting:
/etc/init.d/mysql[19729]: ERROR: The partition with /var/lib/mysql is too full!
When we took a look at the df -h, one of the logical volumes were full. We extended the logical volume using:
lvextend -L30G /dev/VolGroup00/(name)
As the file system needs to be increased, we unmounted the partition using:
umount -l /dev/VolGroup00/(name)

We can't find the partition anymore. It cannot be mounted because it gives us the message:
mount: can't find /dev/VolGroup00/(name) in /etc/fstab or /etc/mtab

/etc/fstab already have the partition listed:
# /dev/mapper/VolGroup00-name
UUID=e894252d-fbe3-4441-8595-09d8a3f1965d / ext3 relatime,errors=remount-ro 0 1

Any LVM command gives the following message:
/proc/mounts: fopen %s failed: No such file or directory
/proc/devices: fopen failed: No such file or directory
What can be done to recover the lost Logical Volume? Any help is appreciated.

1) try to find out if the LV still exists with the command

lvs


the entry in fstab if ok for the root, but maybe the database for mysql is in another LV so if you find something relevant with the lvs command you could try to mount it at the right place. See also 2 for the proc filesystem

for example

mount /dev/VolGroup00/(name) /var/lib/mysql

2) the errors you got could be cause by the fact that proc is not mounted
this could solve it

mount none /proc -t proc


3) Could you resize the filesystem already? in that case a reboot might fix it also.

Thank you, reboot did fix the issue but the logical size still remains the same. The size hasn't changed. How can I resize the logical volume without losing any data?

is there only a single LV mounted at / ?

In this case the problem can bethat you need software from /bin or /sbin which is on the umounted LV.

If this is the problem I see 2 solutions.

1) the most simple one : use a livecd

2) a bit more adventure?

Do this from a text screen (ALT-F3 or whatever and stop as much as possible all services, for instance 'init 2')

mount / -o remount,ro
lvs
lvresize
resize_filesystem (depends on which you use here0
mount / -o remount,rw
shutdown -h now

by remounting the filesystem readonly it remains readable and the changes by the filesystem_resize commands have exclusive write access)

restarting afterwards will make sure everything starts correct and there is nothing cached from before the resize. It shouldn't be needed, but lets play a bit safe here