AutoFill of Dynamic Range

What was the selection at the beginning, it means how many cells did you select from column X when you start to drag over the columns
Else if 2 cells where covered (columns X and Y) then try

Option Explicit

Sub Macro5()
Dim lrow  As Long
    With Sheets("Data03")
        lrow = .Range("A" & Rows.Count).End(xlUp).Row
        .Range("X" & lrow + 1).Formula = "=SUM(X3:X" & lrow & ")"
        'Selection.AutoFill Destination:=Range("X372:BV372"), Type:=xlFillDefault   <---- Recorded with the Excel Macro recorder
        Range("X" & lrow + 1).Resize(, 2).AutoFill Destination:=Range("X" & lrow + 1 & ":BV" & lrow + 1), Type:=xlFillDefault    ' <---- My modified syntax that errors out
    End With
End Sub

Below will do the same..

Sub Macro5()
    With Sheets("Data03")
        lrow = .Range("A" & Rows.Count).End(xlUp).Row
        .Range("X" & lrow + 1 & ":BV" & lrow + 1).Formula = "=SUM(X3:X" & lrow & ")"
    End With
End Sub

and for your query..

Sub Macro5()
    With Sheets("Data03")
        lrow = .Range("A" & Rows.Count).End(xlUp).Row
        .Range("X" & lrow + 1).Formula = "=SUM(X3:X" & lrow & ")"
        .Range("X" & lrow + 1).Select
        'Selection.AutoFill Destination:=Range("X372:BV372"), Type:=xlFillDefault <---- Recorded with the Excel Macro recorder
        Selection.AutoFill Destination:=Range("X" & lrow + 1 & ":BV" & lrow + 1), Type:=xlFillDefault ' <---- My modified syntax that errors out
    End With
End Sub