Well, I'm not a MySQL guy, so the syntax may be wrong here, but I'm thinking the left join is around what you'd want to use.
Something like this...
SELECT a.lidID,
a.familienaam,
a.voornaam
FROM lid a
LEFT JOIN familielidmaatschap b
ON a.lidID = b.lidID
WHERE a.straatID = '37'
AND a.huisnummer = '12'
AND b.familieID != '7'
Though, looking at it, you may be able to just get away with a regular join.
SELECT a.lidID,
a.familienaam,
a.voornaam
FROM lid a, familielidmaatschap b
WHERE a.lidID = b.lidID
AND a.straatID = '37'
AND a.huisnummer = '12'
AND b.familieID != '7'