who makes MX-1 lens ?
MX-1 lens looks to be identical to the Olympus XZ-2 Lens.
Is it a rebranded Olympus lens ?
No is answer to both statement and a question.
Both Pentax and Olympus use third party suppliers to furnish their entry level offer.
Third party suppliers provide them with components and solutions which Olympus and Pentax buy, upgrade, tweak, and brand as they please. It is much cheaper like that, and involves less R&D cost. For example, Pentax has opted to change optical formula a little for its first product done like that.
In this particular case of MX-1 and XZ-2, the third party supplier might be Sanyo (but I'm not 100% sure).
“A portrait is not made in the camera, but on either side of it.”
— Edward Steichen