A common technique for creating lists of unique values is to create a set and pass that set to the list function.
In your boilerplate example, that might look something like:
def drop_down_1_show(self, **event_args):
"""This method is called when the DropDown is shown on the screen"""
searchitem = list({(r['Ejendom'],r) for r in app_tables.inst.search()})
self.drop_down_1.items = searchitem
(I converted your original list comprehension to a set comprehension and passed that to the list function).