The new Ubuntu 24.04 desktop installer doesn't support installing to existing LVM partiton (https://bugs.launchpad.net/ubuntu-desktop-provision/+bug/2058511)

DISCLAIMER: I am not responsible for any damage or negative consequences to your system

However there are workaround that we can use

• Download Ubuntu 24.04 server and desktop installer
  • https://ubuntu.com/download/server
  • https://ubuntu.com/download/desktop
• Install Ubuntu 24.04 server to your existing LVM partition
• Create a autoinstall.yml file
  • Copy the template below
  • Copy the .autoinstall.storage.config section from /var/log/installer/autoinstall-user-data of the Ubuntu 24.04 server installation and put it inside the same section in your autoinstall.yml file
• Boot into Ubuntu 24.04 desktop installer and choose "Try ubuntu" when asked "What would you like to do with Ubuntu?"
• Put the autoinstall.yml file on the live system home folder
• Open terminal and run python3 -m http.server on the home folder
• Open the Ubuntu installer app and select "Automated installation" when asked "How would you like to install Ubuntu?"
• Use http://localhost:8000/autoinstall.yml for the autoinstall.yml URL

References:

• https://canonical-subiquity.readthedocs-hosted.com/en/latest/reference/autoinstall-reference.html
• https://curtin.readthedocs.io/en/latest/topics/config.html
• https://canonical-subiquity.readthedocs-hosted.com/en/latest/tutorial/creating-autoinstall-configuration.html