The target architecture of this fork of LFS is LoongArch. LoongArch is a new 64-bit RISC architecture developed by Loongson Technology Co., Ltd. The software support for LoongArch is still in a very early stage and many aspects of the ABI between kernel and userspace is not stablized yet, meaning it may be impossible to build a system with updated ABI in a chroot environment from a running Linux system on LoongArch but using old ABI. Insteadly, the book is modified to boot the temporary system on the target machine after Chapter 6. So there will be no dependency between the target system and the host after the booting, meaning it's possible to “bootstrap” a LFS system from source using a host with different architecture, removing the need for a running binary distribution for the target machine.
You can find some documents about LoongArch at https://github.com/loongson/LoongArch-Documentation. Note that the documents are not stabalized yet.
On the other hand, the instructions in this book should also work, with some modifications, for other architectures. To cross build a LFS system, the main prerequisite, in addition to those on the next page, is an existing Linux system such as an earlier LFS installation, Ubuntu, Red Hat/Fedora, SuSE, or other distribution. As we've discussed above, this distribution is not necessary to target the architecture you want to build LFS for. Also note that a 32-bit distribution can be installed and used as a host system on a 64-bit architecture.
The default 64-bit build that results from LFS is considered a “pure” 64-bit system. That is, it supports 64-bit executables only. Building a “multi-lib” system requires compiling many applications twice, once for a 32-bit system and once for a 64-bit system. This is not directly supported in LFS because it would interfere with the educational objective of providing the instructions needed for a straightforward base Linux system. Some LFS/BLFS editors maintain a fork of LFS for multilib, which is accessible at https://www.linuxfromscratch.org/~thomas/multilib/index.html. But it is an advanced topic.