According to media reports, the bishop is said to have opened a luxury poultry shop with church funds. He is also said to have taken tables and chairs from the diocesan event room for the premises of his business.
Furthermore, the local newspaper "Sin Fronteras" reported at the weekend that the bishop is listed in the company's documents as a "businessman by profession", one of the founding partners of the company.
The company itself is run under a different name, Manuel Angel Bustamente, who according to the report is connected to the bishop and both were registered at the same address. The bishop avoided commenting on the new allegations.
Last month, after the bishop was accused of having an active sex life, the Vatican appointed Marco Antonio Cortez Lara, Bishop of Tacna and Moquegua, as Apostolic Visitator.
As the Apostolic Nunciature in Peru announced on Monday, Lara is to investigate the two allegations.
Lopez is the bishop of the Roman Catholic territorial prelature in southern Peru, based in July.
A so-called territorial prelature is a particular church that is equivalent to a diocese and has a territorially delimited area of responsibility.
Territorial prelatures are mainly found in South America and Italy.
They are headed by a prelate who exercises the full jurisdiction of a diocesan bishop over the territory.
However, he has often been ordained a bishop.