Yes, you can charge separate lesson charges.
Go to STUDENTS ---> MANAGE STUDENTS ---->ACTIVE STUDENTS. Find the student you want to change the rate for, click on the student, and scroll down to LESSON COST under STUDENT PAYMENT INFORMATION.
Put in the lesson fee and check PER LESSON or FLAT FEE.
The FLAT FEE could be a monthly fee, in which you would put the monthly rate in the LESSON COST.
The PER LESSON is exactly that, and is charged when each lesson attendance is set.
Click on SAVE STUDENT at the bottom of the page and you are done. If there is another student in the same family, locate the other student and repeat the above.