Why does Lewis begin his speech with humor and the request that the students give themselves a round of applause

because he's trying to be funny

Lewis begin his speech with humor to engage the audience and to lighten the mood of the audience.

Explanation:

Michael Lewis started his speech with a perception of humor at the Princeton University and required of the students to award themselves an approval clap due to the fact that he needed the students to perceive that they had attained something worthy of recognition

He needed the students to perceive that they had been diligent enough to be among those that are graduating and to always remember at all times the lessons learnt. In his speech, he intented to relate to the students how favoured they are to have been trained for occupations in the market which unlike when he became a graduate he had little or no preparation for a job.