The behaviors you describe certainly indicate that Lacy lacks confidence and may be easily frightened, but you are enabling these behaviors, and therefore are not helping Lacy to become more confident and relaxed in the world. I would recommend you get in touch with a qualified canine behavior counselor to help you through this process, as there are a number of specific issues that can and should be addressed in a gentle, nonpunitive manner.
Getting Lacy to walk on a leash might be a bit premature if the cause behind this behavior is due to her being frightened when out of your arms. I’d suggest you begin with the goal of her being able to be stationary on the ground, with a leash attached, while you work to help her overcome her fears in general.
A clicker and treats
Using a clicker along with tasty treats in a desensitization/counter-conditioning process will greatly improve her chances of learning to be relaxed. Each time she acknowledges anything in the environment she should be “clicked,” followed by a treat. Begin this process in a relatively calm but new environment; gradually work up to busier environments as her confidence grows. Resist the urge to pick her up, but feel free to sit with her.
I’d also recommend you try a Thundershirt, made specifically to aid anxious dogs. Having a snug wrap around her may give Lacy some comfort, and it certainly won’t do any harm to try.
As for not being able to be left alone, I’d suggest you teach her how pleasurable it can be to be away from you for a bit. You can begin this at home. Resist the urge to coddle Lacy when she can’t seem to function without you. Make it a point to acknowledge her when she isn’t begging for your attention. As flattering as it can be to live with a dog that can’t live without you, it’s ultimately not a healthy relationship.
Be her cheerleader and set her up for success when practicing some independence behavior, by placing a barrier between you – a baby gate or put Lacy in her crate, and leaving something of overwhelming interest to her, like a chew toy stuffed with a tasty bit of peanut butter or cream cheese.
Say nothing as you leave the room or when you return, and always return when she is quiet, never when she’s whining. Begin with very short increments of time, and gradually extend as her confidence in you returning is evident in her calm and quiet behavior.
Of particular concern is that Lacy won’t eat unless you are hand feeding her. I suggest an immediate change, one that will likely be tough for you. Offer two meals a day, and always place her food in a bowl. Place Lacy in a confined space with the bowl, like her crate, and set the timer for 10 minutes. At the end of 10 minutes, the bowl is removed without fanfare.
She may skip a few meals; don’t worry, she’ll survive. Give her no snacks between meals, and leave her alone during meal time. I guarantee that after a few meals have been skipped, she will eventually eat.
A more confident dog
Change your perspective during this process from pity and anxiety to confidence that cutting the “apron strings” will ultimately result in a more confident, well-adjusted dog, and be there to praise and reward her at every small feat accomplished.
In the end, your proudest achievement can be that the dog you love enjoys life to the fullest and that to all who don’t know her story, she appears to be a well-adjusted, confident and happy dog. She was a rescued dog; now she’s Lacy, your wonderful dog.