The Last Of Us ends with Joel saving Ellie and dooming humanity, then lying to Ellie about it. If you want to know more about this ending in detail and my take on it click hear. In this article I will explore, not if I think what Joel did was right (I have already gone over that in the link I have provided), but if Ellie can forgive what he has done.
So can Ellie forgive Joel?
Much like a good joke, this is a question that depends on timing (and misery). Of course if Joel would have told Ellie what happened, after all they have been through, she my have freaked out a bit. I am not sure if she would be more mad that Joel denied humanity the cure they fraught so hard for, or that the group she thought she could trust were going to kill her. This is probably why Joel lies to her, the choice made at the end of The Last Of Us is too much for a child to make, and I think Joel knows this, and doesn't want Ellie to have to face this. I'll bet he plans to tell her, but when she's ready. Of course Ellie won't be able to forgive him, if she never find out what he did. She may suspect something (I would to if I were her) but for all she really knows, they made it to the fireflies, it was a bust, end of story, nothing to forgive.
However if Ellie finds out after she has grown up, and maybe even has started a family of her own. Then she may not only forgive him, but she may even thank him for saving her life, and treating her like a human being, rather than just cargo.
Also even if Ellie found out when she was still young, and did get mad, I don't think she would stay mad.
In The Last Of Us Ellie is not a very rage filled character. Even when she was kidnapped by cannibals, the story never turned into a revenge story. During that whole segment Ellie's goal is not to get revenge on the cannibals, just to get away from them, and get back to Joel.
After the whole ordeal, she even shows remorse for what she has done. She feels bad about killing a bunch of murderous cannibals in self defense. Because of this, it would be very out of character for Ellie to want to harm Joel for what did. Even if Ellie doesn't forgive him she would understand why he did what he did. If she feels bad about hurting people who want to kill her and eat her remains, I don't think she's going to have much against a guy she's come to view as a father, for lying to her to protect her. Especially if she finds out when she's older and more mature, when she has started to form a life again and make new friends, and maybe even start a family of her own. Joel was one of the few people who viewed Ellie as a person, instead of just something to be cut up and experimented on, or even eaten. For Joel and Ellie to become enemies would go against everything the first game accomplished.