Does Red Wedding take effect if there is only a Lord or a Lady in play (i.e. there is not both a Lord and a Lady in play).

No. The effect says to choose both a Lord and a Lady character. In one of each is not chosen, the targeting is not successful, which means the "then kill" part will not take place, which means that the "then claim 2 power" won't, either.

So essentially, if there is not both a Lord and a Lady in play, the plot has no effect.