She's easily my favourite character in the game bar none. Which says a lot because most of the main cast consists of some very well written characters between Hau, Gladian, Kukui, Nanu, Hapu, etc...
I always appreciate when characters go through a major development throughout the story and Lillie is one of the strongest I've seen in the franchise alongside the likes of N, Silver, or ORAS Wally...
At first I didn't particularly care for her because she seemed like she was just a blatantly weak damsel in distress type character that tags along here and there and you have to pull her out of sticky situations. But as the story progresses she literally makes a 180. She starts off as a timid, naive, indecisive, dependant weakling then becoming someone who is more determined, enthusiastic, energetic, confident...more independant...
The first most obvious change we see is her appearance. Earlier in the game she asked if the player chose their own clothes or not and explains that her mother, Lusamine, always made her wear what she chose for her (a very likely reason why Lillie resembles Nihilego since Lusamine was obsessed to the point that she pretty much molded her child to look like the Ultra Beast). Now seeing Lillie wearing what she wants to wear is the first step in her newly found independance as it's something she literally has never done before.
There's also the symbolism with the bridge, at the beginning of the game she could barely move to Nebby's aid. But in Vast Poni Canyon she is able to overcome her fears and cross the bridge. At the beginning she is a fairly weak character too afraid to push herself forward and too afraid to let go of what she knows, but later she is able to move on and cross the bridge towards unfamiliar territory despite what lies in her way.
Leaving behind the past and moving forward into the future.
Then there's her goodbye shows us how far she is willing to go as now she's not only conquered bridges on her own but is willing to travel through a whole region on her own and start her own pokemon journey. We learn later that isn't the only reason behind her leaving but it still shows her willingness to to take initiative since the decision to go to Kanto was 100% her's. Which is something we would never see from the little girl we knew before.
One of my favourite things bout Lillie though are the relationships she has with other characters. Hau, Hapu, Kukui and Burnet, her Mother and Brother as well as the player character and more importantly with Nebby aka Solgaleo/Lunala. It's a dynamic that's only really been explored once from what I recall in previous games (with N and Zekrom/Reshiram) where a major character develops such a bond with the boxart legend.
I love the end credits image featuring Lillie with Solgaleo/Lunala
Maybe Lunala's a little bit more...
As stated Lillie is easily my favourite character in Sun and Moon and she definitely ranks rather high on my list for characters in the franchise as a whole.