Well, as far as I can think of, Fairy Lock is best in doubles/triples battles. Think of this move as Arena Trap, except you will have to use it, and it only works for the following turn. So as useless as it might seem, there are some ways it could be strategic.
1) Klefki, has moderate defensives, and only 2 weaknesses. When against a dragon, dark, or fighting-target, and opponent's best instinct is to switch out, so Fairy Lock can be used to finish them off with multi-target moves such as Dazzling Gleam (+STAB).
2) With this move in play, your allied Pokemon can learn Spd decreasing moves to the opponent. This move won't be very good if you're the last player to move, so consider EV training Klefki in Spd.
3) After Fairy Lock is in play, using moves such as Heal Block and Torment will be very strategic in double/triple battles. Thus giving you the upper hand.
4) Also, Klefki's Toxic can be a very powerful move to ensure you can poison the target, so they don't switch out to a poison or steel type. Also, you can learn Thunder Wave to paralyze the opponent, drastically making you the faster side of the battle. Otherwise, teach similar moves to your allies.
5) Depending on you item and the targets item, you might want to consider using Thief or Switcheroo, depending on your battle style.
Overall, Klefki + Fairy Lock is not a very common strategy used, and it seems as if Klefki more or less turns into a defender or a status move user. But, it all depends on what kind of strategy and team you're assembling.
Hope this helps! :)