"I promise I will find out who did this to you. Even if I have to do it alone."
Lois Lane, 4x01 CRUSADE
Clark: Chloe was my best friend. You're not the only one who misses her.
Lois: I'm just the only one doing something about it.
Clark: ... I get the feeling you like to do things yourself.
Lois wants to find justice for Chloe on her own, or she wouldn't have let herself get run off and turned down by Martha so easily when she dropped by the farm. She's clearly not the type to take no for an answer, and Clark's picked that up already. So when Lois says 'even if I have to do it alone', trying to make it sound as if she's met with with impossible resistance and tried all avenues already, she's revealing her subconscious desire to stand as a single figure against Lionel Luthor, to be the one to bring him to justice herself, against ridiculous odds. Which explains, as well, why she works so hard to get in to see Lionel face to face, when she admittedly has no reason to do so other than to look him in the face - and to let him know who she was, and that she was pitting herself against him. Why does she want to carry this burden alone so badly? Is it just because, as she says, her daddy raised her to be 'independent and self sufficient'?
Rather, it's how she intends to make up for her own 'weakness', in coming to Chloe's funeral, and not being able to emotionally confront her death until three months later. This only seems to be more clearly supported by the fact that she makes the vow literally to Chloe's grave.
Lois: I hate myself for being weak. I just knew that the moment I came here... it would make it real.
And Clark, on some instinctive level, just automatically gets that about Lois. His very first words upon happening across her at the graveside are "You're not alone", and he's the one who invites Lois to stay at the Kent farm and help her investigate, despite his mother having tried to warn her away from going after Lionel, and despite the risk it might pose to his own secret. He knows that if he doesn't work with her, she's going to try to carry it all off on her shoulders, and she has no idea what she's getting into. And he manages to talk her out of her lone crusade in a way that doesn't compromise her pride. As weird as she might think he is initially, and however much they might grate on each other, that gesture lays an immensely solid foundation for a connection between the two.