“Lesser half” refers to the person in the marriage with the least power, in this case the husband.
This term is used to describe the subservient or submissive husband. Typically, spouses refer to each other as their “better half,” often sarcastically. In this case, the sarcasm is taken a bit further by referring to the husband as the “lesser half,” as he is clearly treated by his wife.
"Oh, Lord," groaned the lesser half, "those frying pavements!"
"We have to," was the unshaken response. "Gloria has lost five pounds in the last month and my little girl's health is more important to me than your comfort." (Bobbie)
The conversation also demonstrates distrust and lack of respect for robots, at least on the wife’s part. The husband refers to the robot as a pet.