In the desert region of Moquegua, South Peru on Cerro Baul (2500 masl) i took a photo of these lizard. Does anybody know to which family and genus it belongs ?
In my opinion it is neither a Liolaemus nor a member of the family Iguanidae.
I'd determine it as a lizard belonging to the family Tropiduridae and the genus as Microlophus. If you look very closely at the picture you will see some spine-like scales near the tympynic area (ear), one of the a typical characters for (most) members of this genus. The pattern on the gular region (on the throat) would point towards Microlophus peruvianus, but identification based on photographs without a voucher specimen can be misleading.
Wolfgang Denzer I ended up with Microlophus also - I reply with some reservation also the one on the image have no dark stripes on the dorsal side which M. peruvianus often seem to have. My uninformed guess is Microlophus theresioides which appear to come with local varieties but the species is said to be endemic to Chile. Peru is somewhat to the north yet the same mountain range.
The more prominent pattern on the throat could be male - so is this a female? An image of the ventral side of the lizard shown here should have given further information.
I think the suggestions of Tropiduridae and Microlophus are correct. I would also suggest uploading this image at www.iNaturalist.com. There is a giant community of Herpetologists there who can provide an accurate ID for you.