I want to thank you for committing to Lucy's wellbeing. With minor adjustments to her care, Lucy can live a long and happy life. My EE rooster turned three this year, and his beak is severely deformed.
I believe Lucy's tongue has collapsed. It happens with the muscles that attach it to her mouth don't develop or aren't strong enough to hold it in place. Given how short her lower mandible is, I'm not surprised. It's also not a big deal. Hawke's has collapsed, too. It does present challenges, though, when tube or torpedo feeding.
Personally, I syringe feed my CB. It's just easier and then I know he's getting enough. I make his mash - just so he remembers how to self-feed. I use a special feed since it's hard to grind traditional feed enough so it fits through an oral syringe.
Regarding feeding a mash, when my CB eats, he prefers a soupier mash in a deep bowl. He makes an absolute mess of himself and his surroundings. Be sure to check her crop after she's eaten. If it's hard like an overinflated balloon, she's getting too much air. It should feel squishy - like a deflating balloon.
I don't believe her beak needs trimming. To me, it looks longer because of the parrot-shape and how it looks compared to her lower mandible. I personally would not stress too much about it right now.
