Warning: As always, any time you are messing about with drive partitions, you risk something tragic happening to your data. Backup critical bits before continuing.
First deal with reducing the existing logical volume:
# Boot Ubuntu from live-CD.
# Install lvm2:
$ sudo apt-get install lvm2
# Load the necessary module(s):
$ sudo modprobe dm-mod
# Scan your system for LVM volumes and identify in the output the volume group name that has your Fedora volume (mine proved to be VolGroup00):
$ sudo vgscan
# Activate the volume:
$ sudo vgchange -ay VolGroup00
# Find the logical volume that has your Fedora root filesystem (mine proved to be LogVol00):
$ sudo lvs
# Determine how much space is used on the volume:
$ sudo vgdisplay
# Check the filesystem
sudo e2fsck -f /dev/VolGroup00/LogVol00
# Resize the filesystem to desired size (CRITICAL before proceeding to next step!)
$ resize2fs -f /dev/VolGroup00/LogVol00 16G
# Reduce the size of the logical volume
$ lvreduce -L10G /dev/VolGroup00/LogVol00
Create new logical volumes for /root and /home (in my case /swap already existed):
# First make sure how much free space remains in the volume group
$ sudo vgdisplay
# Create \UbuntuRoot and \home
$ sudo lvcreate -n UbuntuRoot -L10G VolGroup00
$ sudo lvcreate -n home -L18.28G VolGroup00
# Now format the new logical volumes:
$ sudo mkfs -j /dev/VolGroup00/UbuntuRoot -L root
$ sudo mkfs -j /dev/VolGroup00/home -L home
Then run the installer, choosing the appropriate volumes. Note that I had already created a hard partition to serve as /boot --- this is the only way a lvm install will work.
Finally, make sure that the newly installed system has lvm2 included (otherwise it will not start). The following is adapted from here.
# Create a mountpoint for the newly installed system:
$ sudo mkdir /target
$ sudo mkdir /target
# Mount the newly installed system:
$ sudo mount /dev/VolGroup00/UbuntuRoot /target
$ sudo mount /dev/sda6 /target/boot
# Activate those directories and install lvm2
$ sudo chroot /target
$ sudo apt-get update
$ sudo apt-get install lvm2
Now you can restart into the new system!