You need to calculate what is best for you. EU regulation EU261 applies to an involuntary downgrade regardless of reason. Weather would be considered an extraordinary circumstance for flight cancellation or delay compensation but downgrade reimbursement is always due.

If under 1500km this is 30% of the fare paid for the relevant sector, over 1500km to 3500km it’s 50% and over 3500km it’s 75%. If that is more than what you paid, claim EU261 downgrade reimbursement. If the upgrade charge was more, then simply request a refund of that.

If Lufthansa continues to ignore you file a complaint a The LBA, the German enforcement body, or simply put a German lawyer on it. LH have form for delaying and ignoring these claims and will pay up as soon as they realise you’re serious and not going to give up.