When is the schedule change for?
Unfortunately LOT don't respect EC261 rights when it comes to rebooking to other carriers. LOT's rules count 5 hours as the rights of a cancellation, permitting you to a rebooking +/- 30 days on LO metal only.
Do you have a return ticket from HAM? You could complain to the LBA because LOT always opts-out of SÖP as its voluntary. There's no need to bother with the Polish regulator, its got 3 staff and still working on cases from 2020. It's for this reason LOT don't care, as they have no enforcement consequences. Plus, most NEB's have no enforcement power as its based on national law.
In terms of your claim, I would say you have a very good chance of success to sue. Of course I'm seeking of a presumption that LOT will reject your rebooking
. Maybe we will be surprised?
Be sure to contact LOT some more times and make a "Claim" pre-departure on the form online. The waiting period can be several weeks or months, will that be an issue? Ensure your claim is reasonable because you may have to challenge this in Court. So for example, similar flight times, days, that you attempted to reduce costs. Screenshot everything as in DE the Courts pay close attention to this kind of thing. LX or LH is smart cos you could say you were hoping for a Star Alliance waiver. Personally I always go out of my way to get an airline to rebook me before legal action. Calling numerous times, asking for supervisors, emails to public addresses, including CEO. If it all goes to dust, you can show you tried very hard to be reasonable.
I'd appreciate you posting back or following up by PM. I know a few LO agents who I know to be very good, and if they can't help, then you're really at the end of the line!