Apologies for the longer delay this time, but I needed to have a play with a similar scenario since I haven’t worked with LVM.

I set up a VM with Kubuntu (just out of preference; everything else compared to Ubuntu should be the same) and Archlinux similar to your setup (sans LUKS encryption - only wanted to test one thing at a time). I started with installing Kubuntu and letting it do LVM however it wanted, then shrunk it down and installed Archlinux afterwards.

When I was using Ubuntu’s GRUB and letting it do the configuration, it could “find” the Archlinux partition, but it refused to boot it on the basis of “can’t find kernel image” error. Manhandling it produced similar results - it just refused to boot.

Using Archlinux’s GRUB, however, worked flawlessly. It even detected and booted up Kubuntu just fine.

Having a look at the GRUB configuration files, it looks like there’s a difference between the options…

Kubuntu’s GRUB config for booting Archlinux:

menuentry 'Arch Linux (on /dev/mapper/vgkubuntu-archlinux)' --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-/boot/vmlinuz-linux--/dev/mapper/vgkubuntu-archlinux' {
                insmod part_gpt
                insmod lvm
                linux /boot/vmlinuz-linux root=/dev/mapper/vgkubuntu-archlinux rw loglevel=3 quiet
                initrd /boot/initramfs-linux.img
        }

Archlinux’s default GRUB config:

menuentry 'Arch Linux' --class arch --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-simple-42a47177-8802-48bf-93d1-376419d431e5' {
        load_video
        set gfxpayload=keep
        insmod gzio
        insmod part_gpt
        insmod lvm
        insmod ext2
        set root='lvmid/F8XGRm-mOlV-RmRq-sFoj-IBYw-7D8q-lNxCOg/ubT282-XqAq-DvJg-fj4H-bfpQ-1P4f-5215v9'
        if [ x$feature_platform_search_hint = xy ]; then
          search --no-floppy --fs-uuid --set=root --hint='lvmid/F8XGRm-mOlV-RmRq-sFoj-IBYw-7D8q-lNxCOg/ubT282-XqAq-DvJg-fj4H-bfpQ-1P4f-5215v9'  42a47177-8802-48bf-93d1-376419d431e5
        else
          search --no-floppy --fs-uuid --set=root 42a47177-8802-48bf-93d1-376419d431e5
        fi
        echo    'Loading Linux linux ...'
        linux   /boot/vmlinuz-linux root=/dev/mapper/vgkubuntu-archlinux rw  loglevel=3 quiet
        echo    'Loading initial ramdisk ...'
        initrd  /boot/initramfs-linux.img
}

Notice a difference?

Granted, there’s a lot of extra fluff in there, but I noticed that it looks like GRUB has no idea where the root is for the LVM when using (K)Ubuntu’s config. Which is, frankly, just lazy - if you go the other way, Archlinux correctly recognizes the required defaults for booting the other operating system. (I suspect a bug report should be filed, but, eh.)

So, here’s an option:

1. Boot into Archlinux and have it install its GRUB. (Yes, an extra grub installation with grub-install is necessary since the EFI needs to point to the Archlinux install.)
2. Generate a GRUB configuration file within Archlinux. (os-prober should work just fine on Archlinux since I’ve seen their version generating much more workable configurations for other operating systems.)
3. Copy over the theming from Ubuntu’s GRUB into Archlinux’s GRUB config. (This is mostly just for style points - you can theme GRUB however you like).

Hopefully that works a little better.