* American so close to first major 62 * Mickelson lips out at the last hole By Larry King TROON, Scotland, July 14 (Reuters) - Phil Mickelson charged up the leaderboard at the British Open on Thursday, grabbing the first-day lead and a share of the record for the best score in a major championship. Aided by birdies on 10, 14, 16 and 17 on Royal Troon's tricky back nine, the 46-year-old American posted a 63, equalling the record low for majors first set by Johnny Miller in the 1973 U.S. Open. Mickelson came within a fraction of an inch of breaking the record outright. More...