I ended up having to call Mileage Plus customer service. It was very simple: after convincing the agent that Vistara (UK) really is a MP partner (), all I had to do was give him the LOT ticket number. The intra-Europe LH segment was credited instantly, and the UK segment was credited a few days later (he promised "within 24 hours", but I called on a weekend). There was no need to send boarding passes or any other documentation - ticket number was all it took.