Arriving in London on Eurostar on a saturday at 11am and have a 3:15PM flight on Virgin Atlantic to LAX, What is the best and fastest way to LHR,
The fastest and cheapest method is to take the Piccadilly Tube line from St Pancras/King Cross direct to Heathrow. It should take about an hour.
Take the Tube (Piccadilly line) from King's Cross St Pancras to LHR. It will take about an hour and cost £4. See this zoomable map of the Tube system.
I'd also recommend the tube. It is by far the easiest way to go for you. You'll arrive at Heathrow (barring any delays on the Tube, which there seem to be many) with time to spare to check in for your flight to Los Angeles. Alternatively, you could take the tube to Paddington and catch the Heathrow Express train.