Most Lacertid species are quite approachable. Thus, catching lizards for photography purposes makes no sense at all: There’s a high risk of seriously injuring these delicate creatures – Imagine a bird watcher would catch birds for taking pictures! Furthermore, by doing so, you won’t receive satisfying pictures: A frightened lizard will show an unnatural, cramped posture – with rolled eyes like an anxious horse.
Actually, in-situ photography with relaxed "voluntary models" is by far more rewarding. If you act carefully, most species can be quite accessible – and some of them are rather curious so you can get quite close. Some species can also be attracted with fruit and then may act quite tame.
If they disappear in their hiding places: Just come back some minutes later; they may be out again.
It may take some patience. But doing so you’ll have the opportunity of eye-to-eye interaction with a fully conscious, wild animal* – an unforgettable experience!
When you want photograph lizards, try to get at eye-level: This will emphasize the animals' full "personality". (Respectively, only few people photographers would take pictures from a rooftop perspective or a bird's eye view.)
Furthermore, if you get down to the lizards' level, you will appear less threatening and they may be less skittish.
Of course, each photographer may have his own "secrets" for doing portrait shots of these animals.
The requirements on your camera equipment are not too high. The crucial point is flexibility which allows you to do handheld shots: Usually you wont have the time to install a tripod and this may also make too much noise.
For shy species, sufficient focal length could of course help improving your pictures. The more distance - the more natural your models will behave.
Overall, you do not necessarily have to own a camera equipment for several thousands of Euros - with so called "bridge" or "super-zoom" cameras you can achieve acceptable results.
Don't forget: It's not about camera equipment - it's about the photographer...
* We are aware of the fact that using the term "consciousness" is rather problematic. From a scientific perspective, concepts like "consciousness" or "mind" are still poorly defined and hence, the idea of a "conscious lizard" cannot be verified. You may argue that an animal's emotions (like fear, hunger etc.) are just a combination of "instincts" or electro-chemical neuro-reactions. But this would also apply for humans.