[ubuntu] update-grub messing kernels, roots & more upon installing >one ubuntu

I'm testing a few Ubuntu versions before installing and helping with them at the local DIY house where we're building up a digital work shop.
For the record last time I tried to install an Ubuntu 14.04 LTS - Mageia 5 dual boot on a new, physical machine the Ubuntu Grub-install messed up and prevented booting). This time going all *buntu.

To test I'm using qemu/KVM with a virtual disk partitioned with a "physical" (MBR) partition and logicals (LVM).
Note I wanted to test installing the newer release after the "production" version, but went the other way for no good reason.

Using the network install aka Ubuntu MinimalCD I installed
1. Slitaz Linux on a single physical partition (it uses grub legacy if I remember well)
2. Lubuntu 16.04 with /boot on a large physical partition and "/" on lv1 (lvm2): all is fine
3. Lubuntu 14.04 like its older sister with "/" on lv4: grub's borken: found 37 entries of which 29 are broken (full version here [1]). Look how it mixes ubuntu keels...

### BEGIN /etc/grub.d/10_linux ### 
menuentry 'Ubuntu' --class ubuntu --class gnu-linux --class gnu --class os $menuentry_id_option 'gnulinux-simple-51c75e7b-854e-4323-80e1-d24448a826ee' {
  ...
  linux /vmlinuz-4.4.0-22-generic root=/dev/mapper/vg1-lv4 ro  splash quiet $vt_handoff
  initrd  /initrd.img-4.4.0-22-generic                                              
}

### BEGIN /etc/grub.d/30_os-prober ###
menuentry 'Ubuntu 16.04 LTS (16.04) (sur /dev/mapper/vg1-lv1)' --class gnu-linux --class gnu --class os $menuentry_id_option 'osprober-gnulinux-simple-d6a187f0-4ecf-451d-9db9-313e089eb6de' {
  ...
  linux /vmlinuz-4.4.0-22-generic root=/dev/mapper/vg1-lv4 ro splash quiet $vt_handoff
  initrd /initrd.img-4.4.0-22-generic                                            
}

4. Lubuntu 12.04 : grub.cfg now has 22 entries of which 15 ones are broken and misleading [2]

5. eOS 20151213 (based on Ubuntu Trusty): grub.cfg borken; so much that it actually takes half an hour to edit provided we are experts who never make a mistake (obviously #o) and won't break one or more Ubuntu.

Actions I took
6. Booted in Lubuntu 16.04 and ran `os-prober`; it detected the four OSes just perfectly. Then run `update-grub`: found 28 entries of which 14 are broken [3]

I will now try to run `boot-repair` but I wished to ask: What am I doing wrong? and how do you add an Ubuntu to an existing one with a proper grub.cfg?

[1]: https://ptpb.pw/Vdbt
[2]: https://ptpb.pw/DXG_
[3]: https://ptpb.pw/RbeW