Excellent post although unlike the name of the section suggests "Integrate LVM with LUKS encryption", it doesn't really cover how to use LUKS in the context of LVM.
What I mean is you treat LUKS separately from LVM (you start with a new partition). A follow up post describing the usage of both (LUKS encrypted LVM partitions) would be great. Anyway thanks again for this excellent article.
The author article about "How to partition and format a drive on Linux" is also worth reading.