Are you trying to get the result into the cell at the end of the column C? If so, and you are defining Lastrow as a range object then you are right to use the set and that is also why the code I gave didn't work, you would need:
Sub Sum_Last_Row()
Dim Lastrow As Range
Set Lastrow = Cells(Rows.Count, 3).End(xlUp)
Lastrow = Application.WorksheetFunction.Sum(Range("C1:C" & Lastrow))
End Sub