I have done this on other distributions like Void Linux, so I understand the main idea is use cryptsetup to format a luks partition, use lvm to create logical volumes on that partition, install like normal, then set up the kernel and grub to see the encrypted drive and decrypt it. I guess my main question then is how do I add this to the kernel in CRUX? I did find it on the wiki https://crux.nu/Wiki/Cryptsetup, but it seems to be really old. Has anyone done this recently and with EFI? I have tried in the past to set this up following the crux wiki cryptsetup page, I can't remember what part I couldn't get working though I also didn't have too much time back then to mess around with it. One thing that's always confused me in terms of initrd and initramfs is what to pass to the bootloader, because every distro requires different arguments to be passed. I think the simplest bootloader to deal with in terms of LVM on LUKS would be LILO because it has an initrd option (this should also apply to ELILO).
I will explore this as well. I suspect that the main hurdle is going to be setting up an initramfs and setting up a method to update it for newly installed kernels. For building an initramfs and also updating it for newly installed kernels I recommend checking out: https://wiki.gentoo.org/wiki/Custom_Initramfs. From what I know you can make a directory which will house all the files for your initramfs and then point to that directory in your kernel config, so that when you make your kernel (considering you use the same config) your initramfs will be built and/or embedded into your new kernel.