If last resort is your only move..

Question

Will it work?

Answer 1

No. SImple as that.

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

Answer 2

As Rayquaza said no, however there are some ways it is possible.

If you use a choice item like a choice band it will work, and this is as if it was your only move because you're only using it anyway.

If you have 2 moves (e.g fake out and last resort) it will also work then.