Ok, I found the solution and can answer my own questions.
1) can I use LVM over RAID1 on a UEFI machine ?
Yes, definitely. And it will be able to boot even if one of the two disks fails.
2) How to do this ?
The're seem to be a bug in the installer, so just using the installer results in a failure to boot (grub shell).
Here is a working procedure:
1) manually create the following partitions on each of the two disks:
- a 512MB partition with type UEFI a the beginning of the disk
- a partition of type RAID after that
2) create your RAID 1 array with the two RAID partitions, then create your LVM volume group with that array, and your logical volumes (I created one for root, one for home and one for swap).
3) let the install go on, and reboot. FAILURE ! You should get a grub shell.
4) it might be possible to boot from the grub shell, but I choosed to boot from a rescue usb disk. In rescue mode, I opened a shell on my target root fs (that is the one on the root lvm logical volume).
5) get the UUID of this target root partition with 'blkid'. Note it down or take picture with your phone, you'll need it next step.
6) mount the EFI system partition ('mount /boot/efi') and edit the grub.cfg file: vi /boot/efi/EFI/ubuntu/grub.cfg
Here, replace the erroneous UUID with the one you got at point 5.
Save.
7) to be able to boot from the second disk, copy the EFI partition to this second disk:
dd if=/dev/sda1 of=/dev/sdb1 (change sda or sdb with whatever suits your configuration).
8) Reboot. In your UEFI setting screen, set the two EFI partitions as bootable, and set a boot order.
You're done. You can test, unplug one or the other of the disks, it should work !
As of 2019, I was having some issues trying to resize a Ubuntu 18.04 V.M. running on Hyper-V. Installing gparted:
sudo apt install gparted,
running it: sudo gparted
and going through the resizing process on the application's GUI solved my problem.
gparted GUI aid: https://youtu.be/cDgUwWkvuIY?t=330
EDIT: Apparently, this still works as far as Jan/2021 as this answer got upvotes recently.
Best Answer
Benefits
You can think of LVM as "dynamic partitions", meaning that you can create/resize/delete LVM "partitions" (they're called "Logical Volumes" in LVM-speak) from the command line while your Linux system is running: no need to reboot the system to make the kernel aware of the newly-created or resized partitions.
Other nice features that LVM "Logical Volumes" provide are:
If you have more than one hard-disk, Logical Volumes can extend over more than one disk: i.e., they are not limited by the size of one single disk, rather by the total aggregate size.
You can set up "striped" LVs, so that I/O can be distributed to all disks hosting the LV in parallel. (Similar to RAID-0, but a bit easier to set-up.)
You can create a (read-only) snapshot of any LV. You can revert the original LV to the snapshot at a later time, or delete the snapshot if you no longer need it. This is handy for server backups for instance (you cannot stop all your applications from writing, so you create a snapshot and backup the snapshot LV), but can also be used to provide a "safety net" before a critical system upgrade (clone the root partition, upgrade, revert if something went wrong).
While being most useful on server systems, I think that features 1. and 3., combined with LVM's ability to create/resize/delete LVs on the fly, are quite handy on desktop systems as well. (Especially if you experiment a lot with the system.)
Downsides
Of course, all of this comes at a price: the initial setup of LVM is more complex than just partitioning a disk, and you will definitely need to understand the LVM terminology and model (Logical Volumes, Physical Volumes, Volume Groups) before you can start using it. (Once it is set up, using it is much easier, though.)
Also, if you use LVM across hard drives, you may lose all your data when only one drive fails.
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