I'm Dr Marta and I'll try to help you.
What you didn't say was how old Lyttle was and how long you have had her.
Is she comfortable with you holding her? If you can get her to be OK with you she can begin to get more adjusted. Hold her lightly, pet her, lightly scratch her under her neck, scratch her back just in front of her tail. Try brushing her. If she will tolerates this, she may slowly come around and be more friendly towards you.
I've had cats that I rescued that never totally became loving pets. One cat never let me pick her up, never sat in my lap, but sometimes she'd come sit next to me and loved to be brushed and she slept on my bed.
Patience, not making loud noise, talking to her in a soft voice even when she is under the bed.
Sometimes it takes years. Sometimes a cat will never be very social. But if you provide her with a safe home, provide her with love, healthy food, some toys (which she might ignore), clean litter she may turn around.
Don't try to make her go outside unless she wants to.
If you have other cats you may have to separate her from them until she gets more used to the idea that no one is going to hurt her.
I'm sure that you have some questions.
I'll be happy to answer them.