For posterity, I found that localStorage data is stored in a sqlite file called webappsstore.sqlite in your Firefox profile directory. On Windows, this can be found at %APPDATA%\Mozilla\Firefox\Profiles\\webappsstore.sqlite. To read its contents I used a little Python script that uses the sqlite3 package:
import os, sqlite3 profiles = os.path.join(os.environ('APPDATA'),'Mozilla\\Firefox\\Profiles') profile = os.path.join(profiles, os.listdir(profiles)[0]) db = os.path.join(profile,'webappsstore.sqlite') print([entry.encode('utf-8') for entry in sqlite3.connect(db).iterdump()]) (I used Python 3, not sure if there are differences in the Python 2 version of sqlite3.)
This will output a lot of data; I recommend redirecting into a file. The data will be in SQL data creation statements. Each entry in local storage has a domain and key associated with it in a table. The URL is always written backwards in the database. You're looking for something like the following:
INSERT INTO "webappsstore2" VALUES('moc.elpmaxe.www.:https:443','myLocalStorageKey','{"key":"value","pairs":["go","here"]}') You'll find your localStorage key-value pairs somewhere in the output.