The error comes when the range "Target" is more than one cell. Here's one way to deal with that.
Private Sub Worksheet_Change(ByVal Target As Range)
Dim x As Integer
Dim LR As Integer
If Not Application.Intersect(Target, Range("A:A")) Is Nothing And Target.Cells.Count = 1 Then 'only execute if changed cell is in column A and is just a single cell
If Application.CountIf(Range("A:A"), Target) > 1 Then 'check if the number already exists
Target.ClearContents 'clear contents if number exists
'ActiveSheet.Cells(Sheets("lists").Range("I2") + 1, 1).Select 'select the next empty cell
ActiveSheet.Cells(Rows.Count, "A").End(xlUp).Offset(1).Select
End If
LR = Cells(Rows.Count, "A").End(xlUp).Row 'determine last row for time add
If LR < Cells(Rows.Count, "B").End(xlUp).Row Then
LR = Cells(Rows.Count, "B").End(xlUp).Row
End If
For x = 2 To LR
If Cells(x, 1).Value <> "" Then
If Cells(x, 2).Value = "" Then
Cells(x, 2).Value = Time() 'Add the time to the cell if it changes
Beep 'make a sound!
End If
Else
Cells(x, 2).Value = "" 'else clear the time value
End If
Next
End If
End Sub