LM will automatically produce the same schedule for each division with its 'Automatic Scheduling' option under 'Setup' on your toolbar.

Then you can manually change the teetimes for one of the divisions so that matches have different teetimes.

1. Load Division B in.

2. Select MANUAL SCHEDULING on the SETUP menu.

3. Double click any match to change its teetime.

I don't have any specific procedure to randomize teetimes.

For more information, please refer to Manual League Scheduler.