The only legal way of lifting the ball when it lies on the edge of the fairway is when the rules committee of a tournament is playing lift-clean- and place. This would be stated before the tournament began. This accounts for unsavory conditions such as rain. The player is allowed to place a tee where the ball was, clean the ball, and place it back in fairway.
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Yes. Under Rule 28, a player may declare his ball unplayable, and the player is the sole judge of such a declaration.
To remedy the unplayable ball, the player may opt to rehit the ball from the last location, drop the ball behind the unplayable lie on a direct line from the hole through the unplayable lie to the drop point, or drop the ball within two club-lengths of the unplayable lie but not nearer the hole.
However, declaring a ball unplayable is not a free declaration---the player incurs a one stroke penalty (as if the ball landed in a water hazard).
Local rules from the course or club may prohibit this declaration, however. Typically listed as "play the ball as it lies," or similar wording, this would instruct the player to not lift a ball simply due to an unfavorable lie. Violating that rule would incur a two stroke penalty.
Also, to declare a ball unplayable simple because the lie is unfavorable would violate the gentlemanly etiquette of the game of Golf, and is heavily frowned upon.
Read more: Can_you_declare_your_golf_ball_unplayable_by_landing_in_the_rough