I would guess LH would try to get as many people onto the AC flight later that day. Then fly in the following days flight and try to get rid of the backlog that way, eventually the disabled 340 will probably depart empty back to FRA. A few months ago that is what happened.
Keep in mind since LH and AC are Star alliance they could route passengers onward through flights to YVR, YEG, YYZ, and YUL (not too mention even through American Star alliance hubs) to get people to where they needed to go with as little delay as possible.
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