Other answer have pointed to superficial anatomical type differences, but the big issue that really matters is their brain, and how that impacts their psychology and social interactions.
In general, neuroscientists oversimplify vertebrate brain anatomy by breaking it down into three layers, triune brain theory, of Paul D. MacLean from the 1960s. It is an oversimplification and has been superseded by more complex models of the brain, but as a very basic starting point to develop some basic intuitions (especially about the brain differences between different kinds of vertebrates) it isn't a horrible model. As the linked article explains:
The triune model of the mammalian brain is seen as an oversimplified
organizing theme by some in the field of comparative neuroscience.
It continues to hold public interest because of its simplicity. While
inaccurate in many respects as an explanation for brain activity,
structure and evolution, it remains one of very few approximations of
the truth we have to work with: the "neocortex" represents that
cluster of brain structures involved in advanced cognition, including
planning, modeling and simulation; the "limbic brain" refers to those
brain structures, wherever located, associated with social and
nurturing behaviors, mutual reciprocity, and other behaviors and
affects that arose during the age of the mammals; and the "reptilian
brain" refers to those brain structures related to territoriality,
ritual behavior and other "reptile" behaviors.
At the base is the "reptile brain" mostly in the brain stem. This handles most of the "automatic" functions of the nervous system (like breathing when necessary) and also very hard-wired, visceral, almost instinctual responses. MacLean proposed that the reptilian complex was responsible for species-typical instinctual behaviors involved in aggression, dominance, territoriality, and ritual displays. It turns out that this part of the brain is actually present in all vertebrates including fish, amphibians, reptiles and birds, as well as mammals. This part of the brain is fast, reliable, has low metabolic cost relative to return, and gets everything that is necessary for the being with this brain to live done.
Next is the "mammalian brain" which adds the "limbic system" (a term MacLean coined in 1952) and the neocortex, which is responsible, somewhat ironically, with a lot of the aspects of human psychology that we associate with "being human" like love, empathy, parent-child bonding, instinctual fear, and a lot of "gut feelings."
MacLean's recognition of the limbic system as a major functional system in the brain was widely accepted among neuroscientists, and is generally regarded as his most important contribution to the field. MacLean maintained that the structures of the limbic system arose early in mammalian evolution (hence "paleomammalian", with paleo- meaning old) and were responsible for the motivation and emotion involved in feeding, reproductive behaviour, and parental behaviour. Some of the best known components of this system are that:
Septal nuclei: a set of structures that lie in front of the lamina terminalis, considered a pleasure zone
Hippocampus and associated structures: play a central role in the consolidation of new memories
Amygdala: located deep within the temporal lobes and related with a number of emotional processes; and
Nucleus accumbens: involved in reward, pleasure, and addiction
While it is true that non-mammals don't have a neocortex, the distinction isn't as complete and absolute as MacLean originally believed:
While these areas lack the characteristic six neocortical layers,
birds and reptiles generally possess three layers in the dorsal
pallium (the homolog of the mammalian neocortex). The telencephalon of
birds and mammals makes neuroanatomical connections with other
telecencephalic structures like those made by neocortex. It mediates
similar functions such as perception, learning and memory, decision
making, motor control, conceptual thinking.
Still, MacLean was not wrong in the basic direction and source of the neurological differences between reptiles and birds (sauropods) on one hand, and mammals on the other, even though he overstated the completeness and magnitude of the differences.
Finally, there is the "primate brain" which adds the outer cortex that makes up a lot of the volume of the human brain and is associated with "thinking slow" and cold, analytical reasoning tasks like playing chess, doing mathematical proofs, or constructing logical legal arguments. This part of the brain takes up a disproportionate share of a human body's energy consumption, and is slower than either the reptilian brain or the mammalian brain, but is also much more plastic (i.e. capable of being trained or repurposed through interactions with the environment) and more effective at dealing with novel situations. It is the part of our brain that works in a way most similar to how a computer work works, although it isn't as rigid and able to use fuzzy logic and "neural network" type reasoning as well as logical deductive reasoning.
Once of the best ways to illustrate how this presents is to compare a mammalian pet like a dog or a cat or a hamster, to a reptilian pet, like a boa constrictor or an iguana.
When you project human-like feelings of loyalty or affection or trust to a mammalian pet, what you are doing is basically sound. These animals are capable of having these kinds of feelings and have similar nervous system and hormonal hardware that implements their ability to have these feelings.
Reptilian pets aren't like that. No matter how much you think that a big snake or lizard is loyal to you, or has positive feelings towards you, or trusts you, this is just an illusion and when you project these human-like feelings onto a reptile you are engaged in a process of self-deception that does not reflect reality.
No matter how many years of history of you lovingly taking care of it that you have with a boa constrictor or a large lizard, if it is hungry and sees an opportunity to eat you, it will do so with no remorse. This goes beyond simply being wild animals. They simply do not have the feelings that you project upon them. See, e.g. here (8 foot pet python kills owner). They aren't "pets", when you keep them, they are wild specimen animals that you have in your home.
The question is how you want to conduct world building in a way that reflects these neurological differences and reconcile that with your premise that:
these aren't like real lizards because they'll need the following
traits:...
actually like being around humans
can be trained
most importantly, are more intelligent than regular lizards (somewhere
between real-world housecat and Disney animal companion)
All of these traits make the reptiles less "reptile-like", but I want
these lizards to still behave at least somewhat like reptiles.
Greater intelligence and a capacity to be trained isn't really that troublesome as our knowledge of sauropod cognition has improved. You might think of them as on a par with some of the really smart birds, like crows or carrier pigeons, who would have similar brain anatomy and can be trained to some extent. But, unlike curious humans, who are interesting in learning and ideas for their own sake, reptiles and birds learn things more as a means to an end and rarely cogitate and investigate and ponder merely for the sake of doing so.
On the other hand, if they "actually like being around humans" you are really getting into non-reptilian, non-sauropod type behavior. These are types of mental processes that they simply don't have the hardware to experience.
You wouldn't go wrong with portraying lizard people as high functioning psychopaths or Machiavellian personality types, that aren't inherently malicious or antisocial, and who can operate in and even preside over social groups of people, but just don't have emotional empathy at all, even if they can predict from long and careful observation how emotional empathy causes other people to act and respond to their amoral, fundamentally selfish actions that advance their own agendas.
On the other hand, reptiles, unlike even psychopathic humans, don't have a "nucleus accumbens" and therefore aren't driven by pleasure seeking dopamine rush cravings. They want to eat because their bodies tell them they need food. They want to have sex because they need to reproduce. They want to seek the right temperatures because their bodies work better in those temperatures. More social birds interact in a fairly rigid way because they've been hard wired into the benefits or necessity of doing so. But reptiles don't crave dessert because they enjoy eating, don't feel a need to engage in non-reproductive sex merely for pleasure, and wouldn't build sauna's or cold pool spas to entertain themselves with the trill of experiencing extreme temperatures.
To the extent that the cold realities of real life lizards don't suit your story, you might want to shift them to more bird-like behavior, the evolutionary direction in which the dinosaurs ultimately ended up going, but that is still a world away in psychology from all mammals.
