It is resolved!
The idea of modifying the /etc/mkinitcpio.conf file and the kernel did not work.
The solution:
Connect in chroot (I use the live iso Sparkylinux Rescue to do that: https://sourceforge.net/projects/sparkylinux/files/rescue/sparkylinux-2021.03-i686-rescue.iso/download)
We have to set logind-check-graphical=true inside lightdm.conf under /etc/lightdm/
Uncomment the line #set logind-check-graphical=false and change from false to true
We turn off the pc and normally we finally have the lightdm connection window!
For information, I tested an installation with XFCE, we have the same problem because it uses Lightdm!
Thanks again for your ideas. 
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