Custom kernel in Uubuntu live cd

Don't do it unless you know what you are doing.

Not every kernel in ubuntu mainline supports live system

Therefore, choose a kernel which is supposed to support a live system e.g the kernels that comes with ubuntu releases.

If you are experienced enough you can download the source and compile the kernel yourself with live system support enabled. For that, copy a config file from a kernel which already supports live system and use it to compile this new kernel.

All been said and done, installing and inserting new kernel with JLiveCD is easy. Just install them like you install any other package.

I generally use synaptic.

You can run synaptic by simply running synaptic on chroot terminal if it is installed, otherwise install it by apt-get install synaptic

Synaptic is officially supported by JLIVECD, while other software managers are not. The cleaning process for synaptic is done by JLiveCD automatically, while for other package manager, you will need to do the cleaning yourself or those files will lie around there.

Then after exiting the chroot, you will see a prompt like this:

*** ##### Init script & Kernel related #####
Rebuild the initrd if you have 
1. changed init scripts or kernel modules
2. installed new kernel and want to boot that kernel in the live session.

=== Rebuild initrd: (y/n)?: 

Give it y , it will ask the the kernel version, give the correct version (take a look inside edit/lib/modules/ or edit/boot) and you are done; sit back and let it build the iso.

N.B: The same method should work for Linux Mint.