Lucy never says why she allows Natsu to get away with breaking into her room, sleeping in her bed, and everything else he does. Some think it is because of her feelings for him, and while to some extent that may be true, it is not the only reason. Lucy is important to Natsu, she knows that. And while she would like to know on exactly what he sees her as, a job partner, a potential love interest, or just friend, she knows that regardless of which it is she is treasured by the fiery dragon slayer. Natsu may seem childish and ignorant of what his actions mean, but he is not as dense as he makes out to be. That little spark she sometimes sees in his eyes, really just goes to show how devious he really can be.
Natsu has known lose in his life; his birth family, Igneel, and Lisanna are just some of the more prominent ones. He cherishes the things that mean the most to him and lives in the moment, never knowing when that could change. Life as a mage is dangerous, and Fairy Tail isn't known for the cautious nature of its members. That is why Lucy allows his behavior to continue. He needs reassurance that she is there, that she is okay, and will continue to be. She recognizes a lonely soul, when she see one. How can she not, when she sees her own in the mirror everyday.
And really what can she say against him, she knows that she is reassured by his presence just as much as he is by hers. She make act angry and upset, but she knows that he sees the truth. After all this time, if she hasn't actually put bars across the window to keep him out, he should know that he welcome to come to her when the darkness of the night closes in on him and makes him feel alone. That she would never actually turn him out, and that he will always have a place by her side. After all, it is always more fun when they're together, even if all they do is sleep with the knowledge that the other is right there next to them.