Uso de CASE, CUANDO, ENTONCES, FIN en una consulta de selección con MySQL

Select LNext.player As NextPlayer
From lineups As L
    Left Join lineups As LNext
        On LNext.BattingOrder Between 11 And 20
            And LNext.BattingOrder  = Case
                                        When L.BattingOrder  = 19 Then 11
                                        Else L.BattingOrder  + 1
                                        End
Where L.battingOrder Between 11 And 20
    And L.active = 1

De hecho, podrías hacer que se maneje tanto en casa como fuera de esta manera:

Select LNext.player As NextPlayer
From lineups As L
    Left Join lineups As LNext
        On LNext.BattingOrder  = Case
                                    When L.BattingOrder  = 19 Then 11
                                    When L.BattingOrder  = 9 Then 1
                                    Else L.BattingOrder  + 1
                                    End
Where L.active = 1