No, you can't. The move will fail.
Last Resort inflicts damage and has no secondary effect. However, it cannot be used until all other moves that the user knows have been fully executed, at least once, during the battle.
>This counter resets if the user switches out, faints, or the battle ends. Last Resort will fail if it is the only move the user knows.
-Bulbapedia
Last resort will fail if it is the only move the user knows -Bulbapedia