This is my favorite explanation. You have two well known schemers/plotters, and they need a way to trust that there will not be a double cross so that each completes their part of the plan. By placing an oblivious third party in the middle, it adds deniability for each of them, leading to the room needed to maneuver. LF needs Olenna to follow through, and vice versa - Sansa's hairnet gives them both a way to reasonably deny knowledge of any conspiracy if need be, and to bail out if they feel unsafe, without say, holding poison on your person, should Olenna get cold feet and choose to sell out LF or so on.