At the beginning, the Robot is very much limited to his programming, a wealth of knowledge, but not expressing himself all that well - very logical and law-obeying with simple answers ('A-firm-a-tive', 'neg-a-tive'). Yet, by the end of series 3, he is willing to sacrifice himself for the Robinsons and is basically a human in robot form. Throughout the series, we see him bake a cake, fish and even play the guitar, and he regularly cites his programming in many different areas back at Earth. So, getting back to the question, is there actually a definitive point when the Robot becomes more human, or is it just gradual (although I seem to recall a major change from the end of series 1 to series 2, along with the color!)
Interesting question..there are two possibilities for that happening in my view. the latter of the two of course, would be a logical reason.
the first, is that in the science of Lost in space, the robot was built and programmed as a true machine, with many facets of programming, and over time, it developed a personality via his experiences being recorded into his "tapes", ( will Robinson in one episode, refers to Dr smith wanting to erase the Robot's "tapes" and that would be "murder"..we also see in the 3rd season episode "The Time Merchant" The robot is sent back in time to retrieve Smith from earth that he deceived the time merchant into sending him to before the launch. When the robot arrived, his tapes were temporarily erased in the time travel process, and he was as he was in the first half of the first season, and of course to further the plot of this episode, he regains his memory and accomplishes his mission. it seems this kind of robot was created with a gradual learning process and the ability to develop a personality along with its artificial intelligence.
now in reality:
Lost in Space in 1966, was running opposite "Batman", and the batman TV series back then, was obviously very Campy, and quite silly..but it was raking in the ratings, so the story goes that Lost in Space had to do something to compete with it, and they decided to switch from stories of adventure and survival, to an "in kind" ridiculousness that Batman was pumping out..In addition, Jonathan Harris decided to change his character from an evil sneering villian, to a pathetic,laughable, and ridiculous buffoon, as he felt Smith as he was, would have no longevity, and would be killed off or written out sooner or later as the series progressed.. The stories then started to revolve mostly around Will robinson, Dr. Smith and the robot. Due to that also, is why the writers started to make the robot more like a human crew member than just a machine, with emotions, and snappy comebacks to Dr. smiths insults. In fact, once those changes were accomplished, Lost in Space's ratings shot UP, and it was a force to be reckoned with Batman. Unfortuantely, it lost all credibility with most true science fiction fans.
I've been re-watching the show recently, working my way through the first season (the last time I watched it was during its initial run, and have only vague memories of it). I've chronicled it in comments; I think I've seen enough to build my observations into a meaningful answer.
A transformation appears to occur over a few episodes during season 1.
At the start, the robot is essentially emotionless; when confronted with human illogic (mostly from Dr. Smith), or given commands it is unable to execute, its responses have a mildly condescending tone. This tone doesn't suggest an emotional origin, just a dispassionate lack of tact or empathy. For the sake of comparison: on occasion, the computer on the Enterprise D (voiced by Majel Barrett) sometimes sounded a bit condescending too, but it was never ascribed any personality or emotional structure.
At about the tenth episode or so, the robot starts issuing witty comebacks to Dr. Smith, suggesting at least the hint of a personality.
In "War of the Robots" (season 1 episode 20), the robot's behavior can only be explained by emotion - jealousy and mistrust directed at the new arrival, concern over the welfare of the Robinson family, hurt over no longer being needed, despite its denial of having feelings. Some of the robot's lines are delivered with obvious emotive intonation.
In "The Challenge" (season 1 episode 22), the robot laughs at Dr. Smith on a couple of occasions, although it denies doing so. It also holds opinions and a dislike for Dr. Smith, while remaining at least reluctantly obedient to him.
There seems to be no canon explanation for the robot's emergence of a personality - no cause is ever stated or even suggested on-screen, although its apparently emotional behavior is occasionally noticed and questioned by the Robinsons and Smith.
From a production perspective:
These changes coincide with the premiere of the Adam West Batman series. In response to this new competition for viewers, Wikipedia states that the show became more campy. The endowment of a personality to the robot seems to have been part of the show's over-all transformation.