I did not know if the new non-stop flight LAX-SIN would change (or remove) the current schedule of any of the SIA flights (dep LAX).
The first SQ flight is around 9.30 or 10am via NRT - I think this changes with US Day Light Saving finishing, making it an hour earlier departure from LAX which, IIRC, was the reason the opening hours moved to 7.00am a couple of years ago when previously the * Alliance lounge did not open until ~9.00am.