SET @start = '2016-12-12'; -- Новая дата заезда
SET @end = '2016-12-20'; -- Новая дата выезда
SELECT a.nomer
FROM allnomer a
LEFT JOIN main m
  ON a.nomer = m.numbernomer
  AND DATEDIFF(m.datestart, @end) * DATEDIFF(m.dateend, @start) <= 0
WHERE a.type = 'lux' AND m.numbernomer IS NULL
LIMIT 1