If you are in a dispute with someone then you may want to suggest to them that you find a mediator to help. If you are reluctant to suggest this to them, then you may want to find a mediator.
Mediators can approach the other side for you and see if they are willing to mediate.
If you are already working with a lawyer, then they may discuss the option of mediating the dispute with you. They can approach the lawyers for the other side and also work to find a mediator.