The game has instructed me to place Queen Ariad on the board. Queen Ariad only has an ActII Lieutenant Card, but this is only Act I. Do I use her ACTII Card?

As far as I know, you need to use the agent cards and not the lieutenant card if a 'evil hero' is placed by a peril. The lieutenant card is only for the 'evil heroes' placed by the app as you open a door, i.e. when it it is connected to the story.

The game has instructed me to place Queen Ariad on the board. Queen Ariad only has an ActII Lieutenant Card, but this is only Act I. Do I use her ACTII Card?

The peril effect uses the agent cards, use the corresponding card for the act - in your case, the act I agent card.

Thanks.