The alternate install has support for Luks-Encrypted LVM roots. It even has a "Guided" partition mode for encrypted LVM
You will need your /boot partition mounted on non-encrypted media. This means either a separate /boot partition (the "Guided" default), or a USB drive holding your boot partition (if using the latter, you can also store your encryption key on it). This is because your computer cannot execute encrypted code. You need some unencrypted code to unlock the encrypted drive. If you use the USB drive option, make sure you have it inserted and mounted at /boot any time you update. (You could probably make a script to remind you, too...)
A special note: Using a separate boot partition on the same drive to store your bootloader code opens you up to the possibility of an "evil maid" attack, whereby someone with persistent access to your computer can modify your bootloader to record your password, then come back and retrieve it after next time you type your password. If you're just using encryption to protect your files in case of theft, then you don't have to worry about this. If this is a concern for you, keep your /boot on a thumb drive, and keep the thumb drive safe.
P.S: I'm writing this from a LUKS-Encrypted Archlinux system, with a drive that looks something like this:
sda1: /boot - ext2 128M
sda2: LUKS encrypted partition ~300GB
LVM Physical Volume ~300GB
logical volume: /root ext4 296GB
logical volume: swap 4GB
I highly recommend this setup.
Hibernate is working fine, even though swap is on an encrypted partition (but it might not on Ubuntu). If you want a separate /home partition, that's easily done by adding another volume to the LVM. All of this should be achievable from the Ubuntu alternate install.