Are the sentences correct?

Both sentences sound overly convoluted, especially the second one. I would write:

Please pay me the tuition fee on the next (fourth) lesson.

Actually, if the tuition fee is to be paid at the next lesson, why is the word fourth necessary at all? If the next lesson is the fourth, it is implied in the sentence.

"Please pay me the tuition fee at the next lesson" sounds right to me.

Hi Phoenix

In Singapore, private tutors are paid when the fourth lesson comes. They are not paid at the end of the month. The payment is on four-lesson cycles. I hope I've explained clearly enough. If not, please let me know.

Please pay me the tuition fee at the next fourth lesson. (The preposition shouldn't be 'on'. Am I right/)

Many thanks.

After reading your explanation, I believe that a better sentence would be "Please pay me the tuition fee at the beginning of the next lesson cycle."

Actually, my student forgot to inform her mother about the fee. So her mother finally paid me through her maid today, but it was the 6th lesson. This means that the mother paid me at the second lesson of the next cycle. The mother wants to pay me the money for the two lessons of the new cycle, but I want her to pay me the full fee at when the new cycle is complete. This is in order not to confuse matters.

I hope my explanation is clear enough. If not, please let me know.

So could someone please phrase the sentence for me?

Many thanks.

Tell the mother, "Since you have only paid me for one cycle so far, please pay me a full cycle fee at the end of the second cycle."