nowhere do you have a join statement for the categoriesFull, you can use the categoriesFull.CategoryID as a comparison:
AND nominations.CategoriesFullID = categoriesFull.CategoryID
whithout first joining it. try using:
SELECT ScoreID, COUNT(ScoreID) as scoreCount, AVG(Score) as AverageScore, lodges.LodgeID, Lodge, Country, lodges.CountryID, categoriesFull.CategoryID, SW_finalist, SW_rank FROM lodges INNER JOIN countries ON lodges.CountryID = countries.CountryID LEFT OUTER JOIN nominations ON lodges.LodgeID=nominations.LodgeID LEFT OUTER JOIN categoriesFull ON nominations.CategoriesFullID = categoriesFull.CategoryID INNER JOIN scores ON lodges.LodgeID = scores.LodgeID WHERE lodges.CountryID = 3 AND categoriesFull.CategoryID='7' GROUP BY Lodge