No this is the standard reply when you are on an award issued by another carrier - nothing new there. Many other carriers would have replied in the same way (I have no experience with the US carriers you mention)
So you need wait until/if the flight gets cancelled and then deal with it at that time. Yes, most likely you will need to go to the airport to get rebooked; LH call centers agents will refer you to call Avianca as soon as they realise that this an AV award. Maybe LH call center agents can rebook you to the LH flight the next day, but they will for sure refuse to reroute you. The award ticket issued by another carrier makes a big difference there.