Peace in a country depends on the two warring parties themselves wanting to resolve the conflict. That political intention sets the agenda. It becomes a national need. In the Sri Lankan case, this country has enough competence to manage the process. If the two warring parties feel the need for a third party facilitator, then they will invite such third parties to become involved in helping out.
Mediation is based on invitation and consent.
Then there is no question of interference or imposition. There are different types of third parties. The most classical type is the third party with leverage. That is the Indian example - where a big power comes into ensure that the agreement is implemented. There can be different scenarios.