The keys to understanding the ruling are the Definition of 'Lost Ball,' Rule 28, Rule 27-2c, and Decision 27/16.
Both players played their first stroke from the teeing ground into a canyon left of the fairway, an area through the green. Each played a provisional ball from the teeing ground in case the original ball was lost through the green. Lickliter's ball was found and he elected to declare his ball unplayable and return to play another ball from the teeing ground under Rule 28a.
Mickelson asked for search of his ball not to begin, however, when the spotter found a ball, Mickelson was obligated to identify that ball. Mickelson identified his ball and, therefore, was required to abandon the provisional ball and continue play with his original ball (Rule 27-2c). Mickelson also declared his ball unplayable and proceeded in accordance with Rule 28a.
Decision 27/16 states that a player cannot render a ball lost by declaration. The only way a ball can be lost is if it is not found within 5 minutes of the player's side beginning search for it; or the player has put another ball into play even if he has not searched for the original ball; or the player has played a stroke with the provisional ball from a point where the original ball may be lost or a point closer to the hole than that point.
The second issue at hand is the order of play when the player's returned to the teeing ground to play their third strokes respectively. The order of play is determined by the relative positions of the balls before relief is taken (Decision 10/1 is analogous). Therefore, as Lickliter was farther from the hole before the two balls were declared unplayable, he correctly played first from the teeing ground.
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