Generally speaking, teachers are paid for lessons cancelled without sufficient notice. There are instances, however, when a teacher may not be compensated for a last-minute cancellation.
The payment teachers receive for last minute cancellations is compensation for lost time as well as the inability to fill what would normally be a teaching opportunity. This is in the instance that the teacher would normally be available and willing to teach said cancelled lesson.
However, if a teacher has no intention of fulfilling the remainder of their teaching day, they will not be compensated for any lessons cancelled that day - insufficient or otherwise.
For example, a teacher has two in-home lessons scheduled on Monday afternoon. Monday morning, one of the clients cancels their lesson (insufficient notice). Typically the teacher would be compensated for this last minute cancellation. If the teacher chooses to cancel the other lesson because they prefer not to drive for just one lesson, the teacher will not be compensated for the insufficiently cancelled lesson.