How do I install Manjaro MATE with LVM on LUKS and dual boot with Windows?

The most simple solution is to wipe Windows and use then entire device.

The following topic is a script which setup the most simple LUKS encrypted system you can imagine.

The only thing to do afterwards is to put on the toppings - Xorg, desktop, swap, apps etc - but you already expected that since you started the adventure of this thread.