It depends on fitness, age and type of lesson really. A fit horse could easily manage 2 hours of hard work or 3 hours of light/mixed work given appropriate breaks throughout the day. However, this would probably not be needed on weekdays at most yards, so they may have one heavier day a week, and then have days off in the week, and days where they only do one hour/hacking only which is easier on the horse. Obviously if the horse is older or unfit then this would have to be reduced.
I agree with Lovesswimming that most riding schools will have much stricter weight limits due to the amount of work their horses do.
Most riding lessons are really only light work anyway, as even if horses are being asked to jump etc, riders will do this one at a time, and there will be breaks in between. If one rider is doing a course, the others will usually wait in halt. Generally, a horse will usually only have one private lesson/ advanced group per day, and the rest is light work- walk, trot and a little canter at most.
The most important thing is that the horses get a break in order to drink and cool off, especially in this weather.
I know a riding school with fit horses that do 4 hours over a day (with breaks) with days they only do 1 -2 hours and also days off and/or hacking only. They have well looked after fit horses who are fed accordingly and sold after so long in the school. They have strict weight limits as well, stricter than u would have yourself but this is due to the amount of work they do
It would also depend on the age, an what they are doing in the lesson.
At the school where my son and I ride - there are a couple of very elderly ponies who are semi retired - they do max an hour a day - and only once or twice a week, and really just lead rein- very gentle. Just really keeps them busy an moving, but not demanding.
Then there are the younger ponies, who aren't semi retired.... They would do max 2 hours a day, but one would be a less demanding lesson - if one is going to be full on. And they would not do 2 hrs, 5-6 days a week- it would be 2 hrs, 1-2 days a week, then 1 hour 3-4 days a week.