Singapore Airlines would be my choice (carriers on the route: SQ, Garuda, Qatar, Thai, Valuair/Jetstar, Philippine Airlines and Air India). Reasons: decent choice of frequencies and times, aircraft not stopping off en route to/from somewhere else so better likelihood it's on time, and good safety record. You'll likely pay extra for these positives.
(PS I don't think Lufthansa has traffic rights to carry passengers just on the Jakarta-Singapore leg.)