boot – Installation of 18.04 in a pre-existing configuration of Ubuntu 16.04 LVM

I am trying to install Ubuntu 18.04 on my computer.

I have a hard drive that looks like this:

 - sda1: /boot/efi
 - sda2: /boot
 - sda3: [LVM:ubuntu-mate-vg]
   - swap_1
     - cryptswap1
   - /home
   - /

Now when I use USB Live 18.04, it can't detect any existing operating system. What I would like to know: how can I install 18.04 on a new LVM partition, keeping my current configuration working? Of course, I will reduce my existing configuration and make space, but I am concerned: where do I choose to be the boot partition for this new install? Where do I put the root? How would you add it to grub?