why is this a UA issue? UA can only sell/ticket fares that LH makes available to them and you booked through Chase who gave you this misleading, but not false display. If you don’t like how LH implements their classes of services (which is consistent with how other EU carriers do things), then don’t be on a flight operated by LH.

Technically you are able to select a seat, its just for a fee. As opposed to being in a fare that doesn’t allow advance seat selection at all. No where does that display say no fee or complimentary seat selection, which is likely how chase will explain this away. This is no different then UA advertising seat selection on a Y fare, but not having any non-preferred seats (no fee) left. Regardless, UA has no control over how another airline implements their advanced seat assignment fee structure.