Former boss Turner took the reigns on a temporary basis after the Bulls parted company with John Trewick on Monday and his side made a disastrous start as Davide Somma and Matthew Saunders put Lincoln in control after just 20 minutes.
Marc Pugh reduced the deficit three minutes before the break but Hereford, who have now lost five out of six games, conceded again when Saunders netted his second 20 minutes from time to seal victory for the Imps.