The Demon Prince Lt. has the special ability to gain 5 extra conquest when razing a city.

The Ascension plot has the intrinsic effect that the OL receives 5 extra conquest for razing a city.

Does Kar-Amag-Atoth gain 10 extra conquest when playing the Ascension plot upon razing a city?

That's the way we played it. I don't see why you wouldn't. Abilities and special items usually stack in Descent so they would in this case as well.

Here's another question related to the Ascension plot : plot cards are not listed as overlord upgrades on page 24 of the manual (monster, treachery and avatar are the 3 listed under the one per turn rule), but are bundled with overlord upgrades on other pages (p.4 : Plot cards are otherwise purchased in the same way as Avatar Upgrade cards; p.10 : Upgrade examples include Avatar Upgrades, Plot cards, treachery upgrades, and monster upgrades.). Now, even though the manual contradicts itself, we assumed that these cards do count as an overlord upgrade and are thus limited to one per turn. What happens then when you raze two cities in one turn? I don't have the cards in front of me, but what I'm asking is basically : do you have to play the Temple card on the turn you raze the city, or can you play it later?

You play it on a razed city, not when a city is razed.

Thanks for the answer. I was afraid I'd need to raze 5 cities instead of 4 in the end, which looked like a daunting task.