I've now seen the movie, but I was hoping for some clarification. So far, I've seen a few people on Twitter bash Lois for being annoying and useless. I can't speak to what people find annoying, but in terms of being useless is that criticism fair?
Her investigation served the narrative function of revealing a conspiracy against Superman and perhaps even more. If I recall correctly, when Lois is face to face with Lex toward the end she even tells him that she's proven what he did. I suppose since it's not stated explicitly she may not deserve the credit, but is it wrong to assume that her work helped to put Lex Luthor in prison?
She also helped to explain the Martha thing to Bruce as well as assisted with the kryptonite spear. I get that she still needed rescuing because of her efforts with the spear, but no one else was going after it and she was the one who knew where it was. I've seen some even criticize her for disposing of it earlier only to have to go after it later, which I don't understand. When she got rid of it, she didn't know about Doomsday, if I'm not mistaken. So she tried to dispose of it so that it wouldn't hurt Clark again. Then, when she realized there was a Kryptonian monster on the loose, she went after it. She also was able to help a weakened Superman emerge from the water after he went after it.
I know it's not a whole lot, so I can understand some frustration. However, it's just odd to me to see some dismiss all of her time in the movie as useless.