I have a query like this:
SELECT
jobs.*,
(
CASE
WHEN lead_informations.state IS NOT NULL THEN lead_informations.state
MySQL's support is, as you experienced, non-standard. The correct way is to reprint the same expression used in the SELECT clause:
SELECT
jobs.*,
CASE
WHEN lead_informations.state IS NOT NULL THEN lead_informations.state
ELSE 'NEW'
END AS lead_state
FROM
jobs
LEFT JOIN lead_informations ON
lead_informations.job_id = jobs.id
AND
lead_informations.mechanic_id = 3
WHERE
lead_informations.state IS NULL