It is believed that Le Calvez, who was also president and general manager of Le Bristol Paris, departed suddenly.
Philippe Perd, chief project development officer, Oetker Collection, and managing director of Hotel du Cap-Eden-Roc has been appointed to Le Calvez's former roles at Le Bristol Paris.
Frank Marrenbach, chief executive of Oetker Collection, said: "We thank Didier Le Calvez for his contribution and wish him all the best for the future."
Oetker Collection took over the management of the Lanesborough in November 2014 from Starwood Hotels & Resorts, who operated the property under its luxury brand St Regis.
Le Calvez was involved in overseeing the reopening of the Lanesborough in July 2015, following a 19-month renovation costing more than £60m.
Oetker's properties include Hotel du Cap-Eden-Roc in Cap d'Antibes and Palais Maaskar in Marrakech.