What does it mean when a house lord sits in a house counted as the 8th from its own house — like the 7th lord placed in the 2nd house?

Because the 2nd house is counted as the "8th house from the 7th," a 7th lord sitting in the 2nd house is simultaneously occupying a position classical astrology treats with caution. The exact results vary with the sign involved and the Ascendant, but this kind of cross-house relationship is one of the more subtle technical checks astrologers make before judging a house's outcome.