Thanks to everyone for your comments!
After reading this posts, I'm considering to buy a different fork and instead of replacing mine with another one of TREK but made of carbon, since there was no way to know if it was much lighter or not, and since it was on an FX and I don't think they will focus a lot on lightening it, I think the best thing would be to buy one of proven quality and known weight, like a "Ritchey Comp Carbon/Alloy Cross Fork" (540g with uncut steerer).
With that fork I think I can possibly lighten my bike by (almost) 2 pounds or so, which I think is a remarkable amount.
...BUT... that Ritchey fork "axle-to-crown" is 14mm sorter (391mm, when the trek FX forks are 405mm).
I have read that would cause a slight change in the steering angle, making the bike a bit more unstable (which I do not care too much about, since I do not go through difficult terrain and only use it on asphalt), but at the same time, that's better for when you're climbing hills. Is that so, ...isn't it?