Not to be contrarian, but...Lillie didn't really have to work through her traumatic memories. She got them back and all of a sudden could touch Pokemon again and everything was right and fine with the world. I really felt no struggle from that."Lillie gets many things without doing anything for it?" What? Nearly everything Lillie has gotten she has had to work for. She had to work for her close bond with Shiron. She had to work to overcome her fear of touching Pokémon. She had to work through her traumatic memories that caused her fear in the first place.
Before Lillie stepped in to help, the Sandshrew's strategy against Tyranitar was to literally throw themselves at the dragon with hopes of doing damage—which isn't much of a strategy at all. Lillie came up with an actual strategy, and that strategy worked. Lillie may not be an experienced Trainer, but she is very knowledgeable, and she put that knowledge to use. She legitimately earned that Icium Z.
Fighting a Totem Pokémon isn't the only way to earn a Z-Crystal—in the games or in the anime. Lillie helped the Sandshrew defeat Tyranitar, and Sandslash felt that deserved a Z-Crystal.
And I wouldn't call just adding some defense and throwing attacks at Tyranitar a strategy that's any different...