Exercise 3: Can /boot Live on an LVM Logical Volume in a Multi-Boot Setup? — Possible Solution
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Answer: Technically GRUB can boot a root filesystem from LVM, but
/boot itself specifically should NOT be put on an LVM logical volume
-- it should stay on its own small, plain partition.

Explanation:

Per the chapter's own section delivering on grub1-8's deferred
promise, "GRUB can boot a root filesystem that lives on an LVM logical
volume -- grub-mkconfig detects LVM automatically and writes the
correct boot parameters." So the user's distros' own root filesystems
(/, containing the actual installed system) genuinely can live in
separate logical volumes within a shared volume group without any
problem, and this is explicitly named as a genuinely useful pattern
for a multi-boot machine: "each Linux distribution's own root
filesystem can live in its own logical volume within a shared volume
group, letting disk space be divided among multiple distros flexibly
rather than requiring fixed-size partitions decided up front."

/boot is a different case specifically because of when and how GRUB
reads it. Per the chapter, "/boot itself is commonly kept outside
LVM, as its own small, plain partition, because GRUB's ability to
parse LVM metadata directly to locate a kernel and initrd is more
limited and more fragile than reading a plain partition -- especially
once LVM is layered on RAID, or the volume is encrypted." GRUB has to
read /boot's contents (the kernel and initrd images) very early in the
boot process, using its own limited, self-contained code -- before the
full Linux LVM tooling is available to help it -- so a plain partition
it can read directly and reliably is the safer choice, which is
exactly why "Debian's own default installer layout... carves out a
small separate /boot partition even when the rest of the disk uses
LVM."

Recommended setup for the triple-boot scenario:

Keep /boot (and GRUB itself) on a small, plain, non-LVM partition
shared or duplicated appropriately across the setup, while giving each
distro's own root filesystem its own logical volume inside a shared
volume group for flexible space allocation -- exactly the pattern this
chapter names as the practical answer to grub1-8's own deferred
question.

WHY THIS WORKS AS AN ANSWER
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This distinguishes what CAN safely go on LVM (root filesystems) from
what specifically should not (/boot), explaining the real reason for
the distinction (GRUB's own limited early-boot ability to read LVM
metadata) rather than a blanket "LVM and GRUB don't mix."