Firstly - can it be played in joust (I'm assuming so, but that the player to your left is just the player opposite)

more pertinently.

If I play the card, and the other player is choosing the Lord and Lady, whose? is it mine for both, theirs for both or a free choice?

Mighty Jim said:

Of course you got it right, the person to your left is your only opponent in joust.

There is no restriction, so any lord and lady (it would be boring plot otherwise )

You may have some problems with weird situations, so read more

And if there are Lords but no Ladies in play (or vice versa) do you get to choose whether to give them power or death, or is there no event?

You must choose a Lord and a Lady if you want the rest of the effect to take place. If you cannot choose 1 of each, nothing happens.