The commission's concerns centre on reduced competition in the supply of platinum if Lonrho is deemed to have significant influence on Lonrho's mining operations.
The investigation will look into allegations that Anglo's stake may give it sole control over Lonrho and tighten its grip on the world platinum market, where Anglo is already the biggest player.
If the arrangement is ruled monopolistic, the commission could order Anglo to sell some or all of its holding in Lonrho.
In April, the commission blocked a pounds 400m merger of Lonrho's platinum mines with those of South Africa's Gencor, which would have created a platinum rival equal to Anglo.
The development came as Lonrho said investors representing around 54 per cent of its ordinary shares supported the pounds 327m sale to the five hotels to rival hotelier Stakis. Investors holding just under 1 per cent of Lonrho voted against.
Before the extraordinary general meeting called to approve the Metropole deal, Lonrho founder Tiny Rowland again attacked Dieter Bock, Lonrho's former chief executive.
Last month Mr Bock exercised an option to sell his entire 18.3 per cent stake to Johannesburg-based Anglo for pounds 257m and become non-executive deputy chairman. But Mr Rowland has criticised the deal, arguing Mr Bock still has an interest in Lonrho.
Mr Rowland said: "It is a clear conflict of interest for Mr Bock to remain on the board where his knowledge of the company's affairs will help him bargain with Lonrho."
Lonrho denies any secret deal with Mr Bock.Reuse content