No, War Caster doesn't let you do this
Unfortunately, the benefit that War Caster offers is specifically that:
When a hostile creature's movement provokes an opportunity attack from you, you can use your reaction to cast a spell at the creature, rather than making an opportunity attack. The spell must have a casting time of 1 action and must target only that creature.
When you use your action to call the lightning as described by the Call Lightning spell, that's not casting a spell; it's its own special kind of action, manipulating a spell that has already been cast, which isn't covered by War Caster.
You can't use the reaction offered by War Caster to cast Call Lightning as a new spell, either, since Call Lightning doesn't only target that specific creature; the bolt of lightning has an area of effect, so it can potentially target several enemies, even with only the initial bolt, and you can go on to use the spell to affect many different targets over its duration.
For the same reasons it's not valid to cast as a spell using War Caster, I wouldn't suggest houseruling to allow the player to use it this way either. Being able to affect multiple clustered targets gives it a strong advantage over the RAW-legal options available to the caster, as does the fact that it produces an effect more powerful than any cantrip available to the druid but still does not consume a spell slot.