If you had say an 0930 departure ex LAX direct to LHR you would arrive at around 0400 the next morning. If the airlines thought there was a demand for this they would operate such a schedule. It really makes no sense at all to depart LAX until after noon. If however you're desperate to reach LHR as early as possible, depending on how early your client calls you, you can depart LAX at 0935 and arrive LHR at 0635 for that early morning meeting by flying American and routing via Chicago ORD. Multiple other connecting services are also available. So what's the problem exactly?