How to update -grub from live-CD

 In order to update the grub configuration of the machine that you might be misconfigured and unable to boot up properly you could use live CD to boot into the machine, however, even if you are able to update the /etc/default/grub file, you will need to perform the "sudo update-grub" command to effect the change. if you are using Live CD to login, you need to perform the following steps:

First mount the root directory in question for my case it is my /dev/sda so it is it will be /dev/sda2 as mostly sda1 is for the /boot/efi partition.

You will mount the root partition as follow:

sudo mount /dev/sda2 /mnt

Then mount a few more directories that are needed:

sudo mount --bind /dev /mnt/dev
sudo mount --bind /sys /mnt/sys
sudo mount --bind /proc /mnt/proc

How can you tell if you have a boot partition?

Once you have your Ubuntu partition mounted, open /mnt/etc/fstab. If you see an entry for /boot, note which device it is pointing to (/dev/sda4 maybe?). This is the one you have to mount.
Once these are mounted, do chroot to start using the mounted directory as the root partition:
sudo chroot /mnt
You'll get a #/ prompt. First thing to do is confirm that you're using the correct /boot directory. Go to /boot/grub and look at the files there. There should be a bunch of .mod files and a grub.cfg file. If the directory is empty, don't continue, because it means this is NOT your actual boot directory. Look above to see how to determine if you need to mount an additional boot directory.
Once you've confirmed that /boot/ contains the correct files, meaning that it is the correct location, type:
sudo update-grub
This should rebuild your /boot/grub/grub.cfg file with the menu entries.
Then exit the chroot:
exit
At this point you may want to check that things were correctly updated. For this, cd /mnt/boot/grub and check that grub's files are there, there should be a bunch of .mod files and grub.cfg, the latter should have entries for your Ubuntu kernels. If you only see grub.cfg and no .mod files, it means that this is NOT the correct boot directory, look above for how to mount a separate boot partition.
Unmount the filesystems:
sudo umount /mnt/dev
sudo umount /mnt/sys
sudo umount /mnt/proc
sudo umount /mnt/
And then reboot, hopefully your Grub menu will be restored.