To put it mildly, Fudge is a stubborn child and a very difficult little brother for Peter. To answer this question, we need to look at the events that lead up to Fudge's mother serving him lamb chops for dinner. The incident begins when Fudge decides to stop eating, right after Peter learns to do handstands.
By the third day, their mother is concerned by Fudge's refusal to eat, and the family attempts to coerce Fudge to eat in various ways. His father does tricks to entertain him, but nothing works. Only when Peter stands on his head in the kitchen does their mother succeed in getting some baked potato into Fudge's mouth.
Over the next week or so, the family indulges Fudge's ridiculous requests to get him to eat. After that, however, Fudge is taken to the doctor, who tells his mother that Fudge will eat when he gets hungry. This answer wasn't good enough for Fudge's worried mother, so Fudge winds up being taken to other doctors, one of whom suggests that their mother cook Fudge the foods he loves best.
This leads us to the incident with the lamb chops, which are Fudge's very favorite. They were prepared to perfection, and Peter was very jealous that he was expected to eat stew while Fudge got to have lamb chops. However, Fudge's stubbornness and desire for attention prevails, and this is why he refuses to eat the lamb chops.
Throughout this novel, Fudge shows himself to be a selfish, objectionable, and attention-seeking child. The reason he didn't eat his lamb chops was because he wanted to see how whether he could continue to be difficult and how much of his nonsense his parents would take from him.