As others have shared, you can book LH coded, but SQ operated flights between FRA/ MUC and SIN as part of an ABZ-FRA/MUC-SIN itinerary. However, in my experience at least, the lower, "cheapest" Economy fare buckets are not available with such combos and often would start at M fare and then offer B, Y or such. Limited range of Eco fares at best starting the middle price range and then going up towards flexible Y fares. So it'll still cost you.

If you do book two separate itineraries (flight/ flight or train/ flight), I would also leave enough buffer as others mentioned and go as far as following the advice to overnight at airport hotel the night before. We do that as well in such cases and we are not elderly (yet ).