Users cannot be deleted.

Once you create a user, you have the ability to make that user active or inactive, but not to remove the user from the database.
Users must remain to keep the integrity of the history for your database.
Even when an employee leaves your company, you will still want to maintain the historical detail for that person, to know that he or she posted notes, or worked on projects.

To make a user inactive, you will need to have administration rights.
Select the following from Daylite menu bar:

Daylite -> Preferences -> Users & Teams

Highlight the the username and uncheck the 'Active user' box.