Give me some examples of kingdoms where you'd rather open Lookout than Ambassador, and I'll give you a hundred for each one where I'd rather open Ambassador than Lookout*.
Lookout is somewhat random, which makes it get progressively worse beyond the earlygame, as it becomes harder to hit your bad cards with it, and more risky as you might hit only good cards. On top of that, trashing one card is not that huge. Trashing is nice, but not amazing, and the fact it trashes from deck (allowing you to continue buying cards) is marred by how slow it is at trashing. On the other hand Ambassador thins you deck notably faster than Lookout does (typically 2 cards at a time at first, and you often won't buy cards at the same time which while being somewhat of a disadvantage, does mean your deck thins faster), and simultaneously junking your opponent. It takes only a few turns to have a very lean deck while your opponents is full of bloat. On top of that, Ambassador continues to be useful, being usable as a psuedo-curser, throwing out coppers, estates or of course, even curses, right through the mid and often late game, and offers other interesting pile-depletion options and other things right up to endgame, while Lookout becomes a completely dead card.
Finally, Doctor > Lookout for deck thinning, I'd say, in my limited experience. And you can open with two of ANY $3 card, so that's not really a point worth noting...
*Examples may be provided in the form of "Go to goko and hit random 100 times"