Although I hope they lose, strategically I think they should sacrifice Jamie and continue battling. However this is much more about family honor (this all started because of Tyrians arrest) so it will never happen.
Jamie is probably the Lannister that Tywin cherish (if we can say that from such an ice-cold guy) the most. And even if Tywin is not brought to lead with "feelings" he would, for his family "standing" and reputation, NEVER give up on Jamie (he cared to raise an army to crush Riverland for Tyrion whom he most probably despise already).