It follows one of the worst police shootings in South Africa since the end of apartheid.
Police opened fire on striking workers at the mine in Marikana, in the North West province, killing 34 miners.
The shooting took place during a protest by the miners over demands for better pay and conditions.
Prior to the incident, 10 people had already died in the week of protests.
Bishop Jo Seoka said: "We have been in discussions since yesterday and we are pleased to announce that Lonmin have finally agreed to meet with representatives of the strikers."
The bishop sent an open letter to President Jacob Zuma demanding an inquiry into the killing of the miners.
"There is still a huge police presence here today, many of the striking miners are refusing to go back to work, and the miners' grieving families don't know if their loved ones will even get a decent burial," he said.
"The coming investigation into the shootings must commence promptly and consist of an impartial commission that will be able to establish responsibilities for the incident at all levels within the police force and government, and the top management of Lonmin."
Bishop Seoka is also chair of Christian Aid partner, the Bench Marks Foundation, which monitors corporate social responsibility.
The foundation said that the way in which mines in the North West presented themselves often differed from the way communities see them.
"Communities in the area say that mines' corporate social responsibility programmes are 'lies' as they make a lot of promises when they enter a community but often do not deliver," Seoka added.
"The majority of the projects are done to satisfy their public image and rarely do they consult with workers to find out what they actually need."
The foundation warned that a lack of education, training and employment opportunities in the province could trigger further unrest.