Tohono Chull Park and even our patio are home to more Desert Spinys than the surrounding pristine desert - even a little irrigation and a few blooming plants offer access to more bugs than the dry sandy areas with nothing but creosote. Desert Spinys also don't scoff at an occasional bite of a juicy tomato or cactus fruit.
The local population of Zebra Tails is obviously happier where there is more loose sand to dig into - away from walking, ground-compacting feet.
The numbers of Side Blotched Lizards go up and down considerably over the years, and it is not easy to see what triggers peaks and valleys. They happily live around groups of creosote bushes where squirrel holes offer them safety when our local Kestrel is hunting.
Buildings seem to be a great replacement for trees when it comes to the needs of Ornate Tree Lizards. During the years of drought, they certainly fared better close to the house than on the Ironwood Trees where they used to live.
Here on the very west side of Tucson, we have Desert Iguanas. They are big, elegant and very heat tolerant, and vegetarians (partly?). I have seen them climb creosote bushes and even cacti to gnash on flower petals. - They will not appear in masses and eat all your roses, rather they are quite rare and should be enjoyed.
If your area has Chuck-wallas (south Mountain in Phoenix, Waterman Mts) - they also eat plant material. Again, a rarity.
Gila Monsters probably live in more areas than we know, but they are so rarely active, they seem to go out for a very short time every year. But they can finish a whole nest of rodent youngsters or quail eggs in one meal.
The two last photos are not my own, and I cannot find out where it came from. I apologize!
Some relatives of lizards avoid day light. Mediterranean House Geckos live only around buildings where the were introduced. I am surprised that we have them here on the westside of the Tucson Mountains, but they do hang out around our porch lights where bugs congregate at night.
Our Western Banded Gecko is also night active, but stay on the ground while hunting. During the day they hide out in moist, cool spots, often under flower pots, so don't squish the delicate little guy when you move those around.
In summary, what lizards you can 'attract' depends on the habitat and elevation your yard is in - whether you get Earless Lizards or Zebra Tails, Desert Spiny or Clark's Spiny, Regal or Shorthorned Horned Lizards. Like to all ectoterm animals (regulating their body temperature through behavior rather that sweating or shivering), to lizards, hiding and basking spots are both important, as is the structure of the soil (not too much mulching!).
Most lizards need to eat insects, so if you plan to spray against any arthropods, even with insect specific toxins, do not expect a healthy reptilian fauna. If your cats and dogs have the run of the yard, they will disturb and diminish the reptile population.
The very popular decorative crushed rock that covers sterile black plastic foil offers no habitat for anything.
And finally, much of the plastic fencing used to protect plants from herbivores like rats can be a deathtrap for lizards and snakes, who can push through it in one direction, but not withdraw because their scales trap them in those nooses.