I assumed since you wanted to do LVM on LUKS you would have the necessary knowledge to apply before doing the actual install.
The simplest less complicated method I know of uses systemd to boot and it does not involve LVM.
Please bear with me linking to my notepad - while I have published the notes here I cannot remember when or if it was the archived instace - my notepad is there to help me remember.
Direct link to my notepad systemd-boot - LUKS - ext4 | root.nix.dk
Another link using grub Encrypted CLI installation | root.nix.dk
A third - USB stick using grub USB LXDE with persistence | root.nix.dk
While LVM certainly has application in some use-cases - it rarely has application for personal computing - but that is only my personal opinion - and you should use what ever you like - but LVM and RAID I steer clear - instead I have come to appreciate backup, git providers and cloud storage.