How to preserve and freeze modification made during a LiveSession of LiveDisc and to prevent any further modification without remastering the LiveDisc

Custom LiveDisc

Your best choice is probably to create a new custom LiveDisc, but it is a lot of work to setup.

I will suggest a workaround here:

Use a persistent live drive by mkusb and set it up with the desired properties (tweaks, installed programs etc)
Make a tarball of the content in the partition for persistence and store it in some other partition or drive. There is already a tool for it in mkusb, made for backup purposes.
Then you can use the system with persistence

At shutdown you should remove the content of the partition for persistence (if it is important to maintain security and privacy)
Boot into a live (live-only) session and extract the content from the tarball into the partition for persistence ...
and reboot, this time into the persistent live session with the desired properties.

It is possible to do what you want using a modified Guest User account

The install process will ask to remove GDM.

For a grub2 booters with persistent casper-rw partitions, such as mkusb:

Open casper-rw/upper/etc/lightdm/lightdm.conf and change allow-guest=true. Now there will be a Guest account.

For Syslinux booters with persistent casper-rw files such as UNetbootin and Rufus: First mount the casper-rw file:

sudo mkdir /media/casper

sudo mount -o loop casper-rw /media/casper/

Then edit casper/upper/etc/lightdm/lightdm.conf and change allow-guest=true A guest account will be added to boot options.

Modifying the Guest Account

You may use an existing User Account, or create a new User Account, to use as a Live basis for customizing the Guest Session.

Make a directory for guest session, if one does not already exist:

sudo mkdir /etc/guest-session

Create a symbolic link:

sudo ln -s /home/{NAME} /etc/guest-session/skel

Where {NAME} is the name of the User Account you wish to use as a basis.

Any changes made to the user account will appear in the guest account.

Any changes to the guest account will be deleted at end of the session.

User {NAME} can be hidden at login:

See also Add Guest user to Persistent flash drive

Customize Guest Session