I'm new to the Apple world. I was wondering if the update to Lion X will be free for users that has recently bought a new MacBook Pro (like me). If not, how much will it cost?
No, the update will not be free (though it is yet unclear what the price will be, possibilities ranging from $29 to $129), and will only be free for those who purchase computers within 2 weeks of the update coming out (this is usually the time window for the free upgrades that Apple offers) in the summer. If you've purchased your computer recently, sorry, but you'll have to pay for it.
If you just bought your MacBook Pro, you won't be a recent buyer when Lion comes out (it's going to be a few months at least).
Lion will probably cost $129 like almost all OS X updates. (Two versions were less than that: Snow Leopard [10.6] was $29 and 10.1 [Cheetah, I think] was free if you had 10.0, but I doubt the reasons for those two scenarios are the case now.)