I'f Mint is for daily use, I'll assume it controls grub and its configuration files. Remember only one OS has 'control' of GRUB's menu.
To return control to Mint, do this:
1. From the GRUB menu, press c for GRUB's command line
2. Set root with set root='(hdx,y)' where x is the drive and y the partition on the drive where you installed Mint. Remember partitions start with 1.
3. Load the kernel with linux /boot/vmlinuz....... root=/dev/<lvm root device>. If you don't know the version of the kernel, press <tab> for a list.
4. Load the initramfs with initrd /boot/initrd...... If you don't know the version of the kernel, press <tab> for a list. This must match the kernel.
5. Boot the kernel with the command 'boot'.
Once Mint is loaded give Mint control of GRUB again with:
sudo grub-install /dev/sda
Update GRUB's menu with:
If you cannot determine the root device or kernel version, you may also do this:
Mount your Mint partition in Bodhi
mkdir /mnt/mint ; mount /dev/sdx /mnt/mint
where sdx is the partition with Mint
Look at your grub.cfg file in Mint:
cat /mnt/mint/boot/grub/grub.cfg | less
Look for the first menuentry line. Within the menuentry section, note the set root=, linux and initrd lines. Use these as the values for the Steps 1 to 5 above.
I don't use lvm, do I'm not sure of any specifics for lvm.
If this don't work, post back with any error message.