Lumin X1 and headphones amplifier: what to do ?

I forgot to mention that I use my Focal Clear headphone with a 4 pin 
balanced cable.
The headphone amplifier must has this feature.

There are several analog-only headphone amplifiers that accept XLR inputs and have 4-pin balanced XLR headphone outputs, such as those you linked to. I would recommend sticking with that approach as you've stated you want to keep the analog output of the X1.

That being said, the additional feature you probably want is some way to pass through from the headphone amp to your speaker system. As the X1 only has one pair of XLR analog outputs (unless you use RCA for a second set of outputs and switch between the two when you are switching between headphones and speakers—but I think you'd ideally want to avoid that).

Two units I'm aware of supporting what you're looking for, that also provide an exceptionally clean signal path without coloration, are the OPPO HA-1 (discontinued but can still be found) and the Bryston BHA-1. Some people prefer to get the BHA-1 in a "low output" mode for the rear outputs, as the normal output level is too high for their speaker setup.

@nekoaudio 
Many thanks.

I will take a look at the Bryston  BHA-1
My dealer, who sold me the Lumin also sells Bryston.
I don’t know what you mean by ´´low output ´´ mode.
I not very technical.
And yes, I prefer my system  to be all balanced.

Regards