Continuities

The events of Assault Lilys story appear to exist in different continuities' depending on the medium.

"Continuities" are not an official concept established by the franchise creators, but an attempt by fans to catalogue contradictions between the various Assault Lily media and to distinguish the multiple canons of events that they make necessary. The largest contradictions relate to Team Hitotsuyanagi's formation, which has been depicted happening in three very different ways between the first novel, League of Gardens stage play, and anime/game.

At the AK-GARDEN 23 convention, Azone staff claimed that the anime, game and stage plays all "happen in the same world", but neglected to explain which version of Team Hitotsuyanagi's formation is canon.

Novels
The oldest continuity is that of the first two novels, Assault Lily: Move Out, Team Hitotsuyanagi! and Assault Lily ARMS. These novels feature differences in how Team Hitotsuyanagi came together and also the fate of certain other characters.

Some of the doll info pamphlets, like those of the version 1.0 Hitotsuyanagi dolls, also appear to exist in this continuity (as they tell you to go read the novels for more information.)

Stage plays
The stage plays have their own continuity. Most notably, Assault Lily: League of Gardens tells a very different and irreconcilable story about Team Hitotsuyanagi's formation, and the early relationship between Hitotsuyanagi Riri and Shirai Yuyu, from the story that Assault Lily: Bouquet tells.

Anime/game
Assault Lily: Bouquet and Assault Lily: Last Bullet both take place in this continuity (Last Bullet contains a fairly faithful visual novel-style adaptation of Bouquet as an in-game "legion story" for Team Hitotsuyanagi.)

As of chapter 2 of Last Bullet's main story, the line between the anime/game and stage play continuities has become blurry. This part of the game story seems to be written as if most events from the stage plays, such as the battle in Shimokitazawa and the disasters at Ludvico, took place in its continuity. It's not clear at present how these events are meant to fit together.

Starting with The Battle to Overcome and Last Bullet main story chapter 3, stories in Last Bullet explicitly reference the stage plays and vice versa.

Others
The Special Feature on Radgrid contradicts the anime/game in minor ways, such as the listed heights of characters.

The newer webnovels, Assault Lily Glory and Assault Lily Wunder, don't depict any events that would require them to be in any particular one of the continuities suggested above.