It almost never goes far
The single most reassuring fact about an escaped lizard is how unambitious it is. A lizard out of its vivarium is not exploring your house out of curiosity; it is looking for the first warm, dark, tight-fitting space that feels like safety, and that space is usually within a few feet of where it got out. So the first move is containment, not searching: close the door of the vivarium room, block its bottom gap with a towel, and work that room properly before you widen the hunt. Most lizards are recovered from the room they escaped in, and many from the piece of furniture the vivarium itself stands on.
Search the way your species hides
A generic tidy-up will not find it; you have to search as the species. Climbing geckos, crested geckos above all, go up and then still: curtain rails and the folds of the curtains themselves, the tops of wardrobes and bookcases, behind picture frames, the warm top of the vivarium lighting unit. Ground lizards go low and tight: a bearded dragon wedges under the vivarium stand, behind the sofa, alongside a radiator pipe, inside a shoe, or flattened in a laundry pile that holds the warmth of the room. Leopard geckos split the difference, hugging skirting level and slipping into any gap at floor height. In every case, move objects slowly, look before you lift, and check each item of clutter as a potential lizard rather than shaking it out over the floor.
Build a home base it wants to return to
If the first search fails, turn the room into a trap of comforts. Place a hide on the floor in a likely corner with gentle warmth above it, a basking lamp positioned safely or a heat source outside the hide, alongside a small dish of water and the food your lizard finds hardest to resist, live insects for an insectivore. A light dusting of flour across the doorway and around the hide tells you by morning whether it visited in the night. Lizards are creatures of routine, and an escapee that will not be found will often be caught returning, after dark, to the warmest best-smelling spot in the room.
The capture: slow hands, and never the tail
When you do find it, resist the lunge. A startled lizard bolts faster than you can react, and a grab that lands on the tail is a disaster for the several pet gecko species that can shed the tail as an escape trick, leaving you holding it while the lizard disappears, diminished, into a worse hiding place. Work it gently towards a corner or an open tub, then cup both hands around it or scoop it into the tub in one smooth motion. Once it is back in the vivarium, look it over for dust, fibres around the toes and any injury, and let it warm up and calm down before offering food.
If your room-by-room search comes up empty and the lizard may have reached the outdoors, KinsLe's Circle of Love puts nearby pet lovers on notice, so gardens, sheds and warm walls on your street get watched by more eyes than yours alone.