SQLite only has INNER and LEFT JOIN.
Is there a way to do a FULL OUTER JOIN with SQLite?
Yes, see the example on Wikipedia.
SELECT employee.*, department.*
FROM employee
LEFT JOIN department
ON employee.DepartmentID = department.DepartmentID
UNION ALL
SELECT employee.*, department.*
FROM department
LEFT JOIN employee
ON employee.DepartmentID = department.DepartmentID
WHERE employee.DepartmentID IS NULL