You can also say "I request a refund" if you want just the money. But careful, as "refund" is when you ask back for money. So in your case, if you want to ask for another lesson, then you would say something like: "I want to reschedule the lesson I had technical difficulties with" if you want to change the whole lesson. In addition, if you want to mention about money, simply add "And I would like to request a refund".

It is a refund request. A refund is when you buy something from somebody. An example of a reimbursement request is when you spend your own money on behalf of your company. Later, you request a reimbursement from your company. You request your company to pay you back the expense that was done on its behalf.