Theme cached files are being updated using the API token's User:
// Find user settings for owner_id linked to API token used in request
$userSettings = new UserSettings(User::find($token['owner_id']));
$userTheme = $userSettings->get("edit_theme")['code'];
This is wrong, and was missed in testing. Instead, the theme should always be based on the lemonsync.json's "theme_code".