Even if there is no regular immigration check when travelling between Schengen countries, German alien law requires you as a non-EEA citizen to have a valid passport when entering Germany, also when crossing an 'open' border from another Schengen member state. Since Netherlands is one of the main sources of illegal drugs and narcotics in Germany, I have the impression that customs checks are more likely when entering from Netherlands than from many other countries. If you are picked for a random check, German customs is likely to ask for your passport as well.
I have never flown with Lufthansa from Amsterdam and practice may differ from airport to airport, but the last few years, I have never experienced an id check when flying with Lufthansa on intra-Schengen flights from other airports. According to Lufthansa's 'General Conditions for Carriage' §13.2 you are however expected to be able to present all travel documents required to enter the destination country, which in this case is a valid passport.