I don't care what language it comes from. It sounds just like Alex and looks just like a creative version of it, and in fact the one Alix I ever knew used it as short for Alexandra.
Alix being a form of Alice and not Alex is not important today in any context except a linguistic/scholarly one.
"It's one thing to be open-minded and quite another to be so open-minded your brains fall out."--Dear Abby
"Let other people push you around, and you deserve whatever bad things happen after that."--Lauren Bacall