The only purpose of an initramfs is to mount the root filesystem. The initramfs is a complete set of directories that you would find on a normal root filesystem. It is bundled into a single cpio archive and compressed with one of several compression algorithms.
At boot time, the boot loader loads the kernel and the initramfs image into memory and starts the kernel. The kernel checks for the presence of the initramfs and, if found, mounts it as / and runs /init. The init program is typically a shell script. Note that the boot process takes longer, possibly significantly longer, if an initramfs is used.
For most distributions, kernel modules are the biggest reason to have an initramfs. In a general distribution, there are many unknowns such as file system types and disk layouts. In a way, this is the opposite of LFS where the system capabilities and layout are known and a custom kernel is normally built. In this situation, an initramfs is rarely needed.
There are only four primary reasons to have an initramfs in the LFS environment: loading the rootfs from a network, loading it from an LVM logical volume, having an encrypted rootfs where a password is required, or for the convenience of specifying the rootfs as a LABEL or UUID. Anything else usually means that the kernel was not configured properly.