オブジェクト指向…
奥が深い…

魔界の仮面弁士様のコードを参考にして…

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    Private Sub lblMoving_MouseEnter(sender As Object, e As EventArgs) Handles lblMovingUp.MouseEnter, lblMovingDown.MouseEnter, lblMovingLeft.MouseEnter, lblMovingRight.MouseEnter
        Select Case sender.Tag
            Case "UP"
                lblMovingUp.BackColor = Color.LightPink
            Case "DOWN"
                lblMovingDown.BackColor = Color.LightPink
            Case "LEFT"
                lblMovingLeft.BackColor = Color.LightPink
            Case "RIGHT"
                lblMovingRight.BackColor = Color.LightPink
        End Select
    End Sub
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これも…
↓
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    Private Sub lblMoving_MouseEnter(sender As Object, e As EventArgs) Handles lblMovingUp.MouseEnter, lblMovingDown.MouseEnter, lblMovingLeft.MouseEnter, lblMovingRight.MouseEnter
        sender.BackColor = Color.LightPink
    End Sub
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こうなりましたｗ

プログラム的には
DirectCast(Sender,Label).BackColor
…とした方がスマートなのかも知れませんが…