Another option
Sub LookupCopy()
Dim InAry As Variant, Oary As Variant
Dim i As Long
With Sheets("sheet1")
InAry = .Range("A1", .Range("A" & Rows.Count).End(xlUp).Offset(, 1))
End With
With Sheets("sheet2")
Oary = .Range("A1", .Range("A" & Rows.Count).End(xlUp).Offset(, 1))
End With
With CreateObject("scripting.dictionary")
For i = 1 To UBound(InAry)
.Item(InAry(i, 1)) = InAry(i, 2)
Next i
For i = 1 To UBound(Oary)
Oary(i, 2) = .Item(Oary(i, 1))
Next i
End With
Sheets("sheet2").Range("B1").Resize(UBound(Oary)).Value = Application.Index(Oary, 0, 2)
End Sub