Having just watched the episode "Code of Honor" from Star Trek: The Next Generation, how come upon meeting Lutan, Troi sensed his avarice, ambition and a strong desire for Tasha, but said nothing? She even told the others later that she'd sensed it, and no one pulls her up on it!
You're conflating two separate things that she sensed; Lutan's strong and extremely obvious attraction for Tasha Yar (which pretty much everyone noticed, regardless of their empathic ability) and Lutan's personal desire for power and influence.
Frankly, the first wasn't worth mentioning. Troi herself notes that Yar is a very good-looking woman and that strong feelings of lust to her were coming from all the men present.
TROI: ...Some sexual attraction from all the males. Lieutenant Yar is physically very attractive.
and while she might have mentioned that Lutan was an
avaricious and ambitious
man, giving that information to Picard would be like telling the Captain a Romulan visitor is "sneaky" or that a Vulcan is "cold", it's nothing he doesn't already know or couldn't guess on his own.