Hey there. I got you message and sorry for the late reply. I actually don't know a lot about LVM, but the general idea applies: You need to have your mountpoints referenced in /etc/fstab.
above is the example of my fstab. You'll need to have in your a line for /boot, /, and swap in order to correctly boot the system. The error you are receiving is that the system doesnt know where to find initramfs because you haven't told it where /boot is in fstab i think.
% cat /etc/fstab
# /etc/fstab: static file system information.
# <file system> <mount point> <type> <options> <dump> <pass>
proc /proc proc nodev,noexec,nosuid 0 0
#Entry for /dev/sda5 :
UUID=f69e96f4-8a45-4921-8778-48c83947e226 / ext4 errors=remount-ro 0 1
#Entry for /dev/sda7 :
UUID=ceeb74c2-629c-499e-b900-ce7df2715aca /boot ext2 defaults 0 2
#Entry for /dev/sda6 :
UUID=c52bf6fa-061a-4917-a47c-506afe6d7ffe none swap sw 0 0
you can manually edit /etc/fstab and add the above lines like in mine, but change the uuid to the referenced disk. My guess is the ext4 partition above is / and the ext2 partition is /boot (as that is the default). though please properly mount the lvm in livecd and check the uuids/partitions.
edit: i found this that might help you map fstab correctly for lvm. you can use devs instead of UUIDs
duxon@rolfgang:~% cat /etc/fstab
# /etc/fstab: static file system information
# <file system> <dir> <type> <options> <dump> <pass>
/dev/mapper/main-root / ext4 rw,relatime,data=ordered 0 1
# /dev/mapper/main-home LABEL=home
/dev/mapper/main-home /home ext4 rw,relatime,data=ordered 0 2
UUID=91d776eb-1cf4-4437-a06e-f6a86ee7d0fb /boot ext4 rw,relatime,data=ordered 0 2
UUID=6ccf4f96-a05f-4e71-b864-7652e3684c23 none swap defaults,discard 0 0