You are almost certainly thinking of "mediation." Mediation is an alternative process in which the warring parties try to come together to resolve their dispute without a trial. Usually lawyers accompany their clients to mediation, and there is a neutral mediator whose job it is to help the parties to reach agreement IF agreement can be reached.
When lawyers bill their clients for their time, time spent attending a mediation is no different than time spent doing other things. It's all work done on behalf of a client.
Not legal advice as I don't practice law in Indiana. It's just my two cents on the facts you describe in light of general principles of law. If you need legal advice, please consult a lawyer who holds Indiana licensure. That's not me.
Mediation is a form of alternative dispute resolution in which a third-party who is neutral in the case - typically a lawyer- trys to get both sides to come to an agreement to settle a dispute before litigation begins or escalates. In Indiana, some court matters are required to go through mediation to see if the parties can negotiate in good faith to resolve the dispute before the matter goes to trial. The cost of mediation is usually split between the two parties and the cost can vary.
Advice on this forum is for informational purposes only and should never be mistaken as a substitute for legal advice. If you are in need of legal advice, you should consult local legal counsel.