I was looking into the MPN flights using Avios a few weeks ago while planning a trip to the Chile and came up with nothing. I have no knowledge of how the LanPass program works in regards to the basic low level redemptions and an 'anytime' sort of redemption when using a greater amount of miles, but I (correctly or not) attributed a lack of availability using Avios to the lowest 16000 km one way awards not being available from LanPass.
The complete lack of award space for partners is a big change from even less than a year or so ago, when award space was plentiful when looking far ahead in advance.