Adding LUKS hard disk encryption on LVM after the fact

I have an external hard disk enclosure with two disks. I used Logical Volume Manager to create a single logical volume that spanned them, and slowly filled it to about 60% capacity. Lately, I’ve been trying to be more conscious of using encryption, and this was one area where I hadn’t done so. At the time I felt like learning how to do LVM was enough, and LUKS could wait until later.