We do not allow deletion of event pages in LaunchTrack, even if the event has past and you don't plan on using the event page again.
What you can do instead is Archive the event so that it's hidden from public view and people can no longer register for the event.
That way, you have all the benefits of deleting an event (hiding it from view and preventing new registrations), as well as the benefits of *not* deleting it - For example, there might be valuable event, customer, and/or payment data tied to the event that you might have to refer back to in the future. (You never know...)
For more details on how to Archive an event, click here.
Here's another benefit of Archiving old events: If it's a recurring event (for example an annual event), then you can always Archive the event and keep it hidden away once it's finished, and then when the time comes you can "Copy" the old archived event and update it the following year to save yourself a lot of time. (Assuming the event stays relatively similar from year to year)