You have not told us your class of travel but:
LH425 BOS-MUC on 21 Dec and LH761 DEL-FRA on 4 Jan appear to be very full and depending on the class of travel it’s not possible to book on these flights. I tried a dummy booking on LH425 and could book a business seat but not economy. On LH761 I could book an economy seat but not business. However, It looks like all flights are operating.

I think the LH app is very buggy. More so than the website.

Speaking of LH app I stupidly downloaded Lufthansa beta app. When I tried to check in for a flight for tomorrow I got stuck when the app started asking me for entry documents for Germany. I have’s entered (only transited in) Germany since Brexit but I shouldn’t need any. Fortunately I still have the non-beta version of the app on my iPad so I was able to check and found I was already checked in. Has anyone else downloaded Lufthansa beta app?