[lubuntu] grub2 setup errors on external drive; can boot manually

Lubuntu (I actually installed 16.04 Beta1 rather than 15.10 like I usually would, just to get at keel 4.4) did install correctly to this drive during the install process, but because grub2 and UEFI and exteal USB hard drives are such a rat's nest, I can't get it to set up grub2 correctly.

I've managed to get as far as the boot entry taking me to the grub2 command line, and from there, I can point it at the correct linux keel and initrd images and manually boot. From that point on, everything's fine. But I'm at a loss for how to actually get grub installed correctly so I don't have to keep doing that every time.

Some stats:
The PC itself is a Quantum Byte (32-bit Windows 10, Atom Z3735F, 2GB RAM), which means 32-bit UEFI. Lubuntu is 64-bit because the Z3735F is a Silvermont and mixed-mode UEFI has been supported by both the keel and by Ubuntu (and kin) for a while now.

The output of sudo update-grub2:

$ sudo update-grub2
Generating grub configuration file ...
Found linux image: /boot/vmlinuz-4.4.0-13-generic
Found initrd image: /boot/initrd.img-4.4.0-13-generic
Found linux image: /boot/vmlinuz-4.4.0-7-generic
Found initrd image: /boot/initrd.img-4.4.0-7-generic
blockdev: ioctl error on BLKROSET: Operation not permitted
Found Windows Boot Manager on /dev/mmcblk0p1@/EFI/Microsoft/Boot/bootmgfw.efi
Adding boot menu entry for EFI firmware configuration
done

My main reason for installing to an exteal hard drive is that the eMMC storage in this PC is only 32GB, and Windows (along with the other programs I use and the massive size of VS Community 2015) takes up all but ~6GB of it. So having Lubuntu on the exteal drive is nicer: the partition breakdown on the exteal is:

1GB FAT32 EFI System Partition
20GB ext4 /
2GB swap
25GB /home
30GB NTFS shared storage