If the lessons were always inside a CellGroupBy unit (e.g. an hour), you could use smaller units for time cells (e.g. CellDuration=15) and hide some of them:
http://www.daypilot.org/scheduler-hiding-non-business-hours.html
However, this doesn't seem to be the case (10:15 - 11:15). I would probably store lesson order number as the hour part of the start and end and override the time headers using BeforeTimeHeaderRender.
Example:
Lesson 1: start 2011-09-12T00:00:00 end 2011-09-12T01:00:00
Lesson 2: start 2011-09-12T01:00:00 end 2011-09-12T02:00:00
etc.
CellDuration=60
BusinessBeginsHour=0
BusinessEndsHour=6 (for 6 lessons a day)
ShowNonBusiness=true
BeforeTimeHeaderRender:
protected void DayPilotScheduler1_BeforeTimeHeaderRender(object sender, DayPilot.Web.Ui.Events.BeforeTimeHeaderRenderEventArgs e)
{
switch (e.Start.Hour) {
case 0: e.InnerHTML = "9:00 - 10:00"; break;
case 1: e.InnerHTML = "10:15 - 11:15"; break;
// etc
}
}