The Bugsnax Liz missing diary pieces come into play when you meet Eggabell in the Frosted Peak, as she will ask you to get four of Lizbert’s items before you can proceed. This is part of the quest called ‘Crack The Code’, and all four pieces are needed to progress in Bugsnax. Three of these items are earned by getting the villagers back to camp, while the fourth can be found in the open world itself. Here, you can find what quest each item is linked to, how to complete those quests, and how to collect all four of Liz’s items for Eggabell.
Find Lizbert's Journal
This is given to you by Triffany once she has returned to Snaxburg and been interviewed. To get her to return, you’ll need to open the Hidden Ruins in the Scorched Gorge.
However, to open it, you’ll need the diary key, which you’ll get off Gramble after his own interview. He returns to Snaxburg after you have mastered controlling Sprout, which you’ll demonstrate with the obstacle course and safe return of Orange Peelbugs and Kweebles in the Simmering Springs.
Gramble will return to Snaxburg first, but you can interview them in either order.
Find The Missing Page
Unfortunately, even with the diary, you won’t have the full picture yet, because there’s a missing page. This one is probably the trickiest piece of the Crack The Code puzzle to solve, as it’s less straightforward than simply interviewing people.
First, you need to bring Triffany back to Snaxburg. You do this by entering the Hidden Ruins in the Scorched Gorge. When she’s back, interview her and get half of the diary page.
Next, you will need to bring Cromdo back to Snaxburg. To do this, you have to complete what amounts to a tutorial for the Launcher, and will also need to bring him two Big Bopsicles. You catch these by covering them in Chocolate in the Sugarpine Forest and waiting for a Charmallow to land on them, melting them so they can be caught. Cromdo, like Triffany, is also found initially in the Scorched Gorge.
Never a man to give away something for nothing, Cromdo will not give you the reward after his interview, but will instead keep it until you have completed his side quest, which ends with catching the Mothra Supreme. To do this, you’ll need to talk to Cromdo in Snaxburg and do various sneaky favours, stealing from other huts. Eventually, you’ll follow Cromdo to the Sizzlin’ Sands, where the Mothra Supreme appears. Wait for him to activate the statue, then use the Launcher to hit the Mothra Supreme with Bombinos, using the Grapple Gun to pull the pizza slicers down on top of the downed Supreme. Do this twice, then the final time you’ll need to place the Bombino under the Mothra Supreme so it gets taken by the tornado. This will end the quest, and talking to Cromdo back in Snaxburg will see him give you a map to a secret location at the far end of Boiling Bay, beyond the shipwreck.
Go here, and you will find a backpack containing the missing page.
Find Liz's Device Notes
This one’s nice and easy. As part of the game’s opening tutorial, you will bring both Filbo and Wambus back to Snaxburg. Once they’re back, interview Wambus and he will provide you with the device notes. Typically, this will be the first clue you get in the whole game.
Find Notes on the Mountain Map
The final item you need to give Eggabell comes from Snorpy. Much like Cromdo, he gives you a new tool (two in fact, with the Trip Wire and the Grapple Gun), and you will need the Trip Wire to trip and then catch the first ‘snak he requires, a Kwookie. After this, he needs a Charmallow, which can be lured to a Big Bopsicle with Chocolate to extinguish it. Snorpy and Chandlo are a pair, so you’ll also want to catch Cinnasnails and (with help from the Grapple Gun) Hunnabees to get Chandlo ready to head back home. With all this done, Snorpy will give you a mountain map once he has been interviewed.
When you've got all of this, you should be able to approach and open the mystery door. Voila!