It is possible to have some fun during the lesson. There is the interaction between the teacher and the student and opportunities for a joke, or to share a lighter moment, or to share the humour in something a bit unexpected. Sometimes it is appropriate and helpful to discuss a topic not even related to music.
I welcome these brief diversions during my lessons. They are an opportunity for the student, and the teacher, to relax and give our brains a rest before once again concentrating on the lesson. They also help to build rapport with the student.
But I don’t claim that my lessons will make learning fun because the fun bits are not usually when the teaching or learning happens.
I do aim to make lessons interesting, satisfying plus a little challenging. I want the student to feel that the lesson was enjoyable and worthwhile