You've been given great advice. The most important thing to remember is that every budgie is an individual, and the only way to earn their trust and build a bond is to always go at their
pace, and never rush them. Patience, love, and respect are key. Hanging out with her in the same room, talking to her, sitting by her cage, reading to her, involving her in your life in every way possible WITHOUT forcing her out of her comfort zone will tell her the message that you are her flock member and that she can trust you.
Every day, you've been rushing her and trying to go from stepping up to petting, all in one day. This is a process that can take months!! Even putting your hand OUTSIDE of the cage on the bars should be done before, slowly and surely, every day consistently, so she knows what to expect, isn't frightened by you and can gradually learn to trust you. After a long time, she'll be more comfortable in her cage even if you hand is on the outside of the cage. Then you can put your hand in the cage, just rest it there so she can see it, and do that a few times a day for a long time, weeks or months. You slowly proceed from there, always making sure she knows that you aren't going to frighten her, taking as much time as she needs until she opens up around you and doesn't mind your presence. You don't have to touch her to build a bond, either. As mentioned above, while you work on getting her used to your hand over the next few months, you should involve her in your life, talk to her, sing to her, etc. as mentioned above. She will become more comfortable over time!
As Sweety's mom said above, a bond can look like a lot of different things. Comparing your progress to things you see on the internet is counterproductive because it not only never shows the whole picture (some birds are "submissive" out of fear and not because they are trusting of their human
) but it also doesn't accurately represent your Lili and what her personality is like
Don't give up! You've got this~