if the liberators defeat and kill Octavian, I give them a 90% chance of winning the battle. Their morale will skyrocket and they will gain lots of loot. This leads to less impatience and fewer desertions amongst their men, critically the mercenaries. This (and Cassius' survival) then leads to Brutus not being forced to attack when he did. This leads to the news of Admiral Ahenobarbus' victory over the triumvir fleet vest of Greece reaching the liberators and the realization on their part that Marc Anthony is for all intents and purposes trapped and running out of supplies. This enables them to keep their army in check, while this time its Anthony's men that begin deserting.
You thus end up with a situation that corresponds perfectly to Brutus' and Cassius' original battle plan, of having a starved enemy charge their fortified positions. while stranger things have happened, I doubt Anthony will be able to snatch a victory in these conditions. Moreover, he wont be able to retreat his army to Italy directly, but instead have to use the long route up the Adriatic coast on foot due to the triumvir fleet being defeated. Brutus and Cassius thus have a very good shot at reaching Italy before him, or trapping and destroying him altogether.
Lepidus might try and fight, but he's not really a leader and doesn't have many troops anyway, since Octavian and Marc Anthony took most of them to Greece. What he might do is possibly hand over the keys to Rome in exchange for some sort of position in the future government, or at least semi-retirement like was forced upon him by Octavian OTL.
Sextus Pompeius controls Sicily and a considerable fleet at this point, and might try and take Rome, but its a long shot given everyone will want to ingratiate themselves with the victors in the east. Most likely a political settlement will be reached between him and the Liberators, possibly setting the stage for another round of civil wars several years down the line.
If he does try and fight, he simply can't match the resources Brutus and Cassius have at their disposal. Any war between him and them will probably be very similar to the one he fought against Octavian and Marc Anthony, with the same forgone conclusion