The sentence requires a quantifier that can be used with a countable noun like 'friends'. 'Much' is used with uncountable nouns. 'Many', 'lots', and 'a lot of' can all be used with countable nouns. However, 'lots' is more informal and often used without 'of'. 'A lot of' is a common and grammatically correct choice here. 'Many' is also correct but 'a lot of' fits well in this context. The most appropriate and common choice is 'a lot of'.
The correct answer is a lot of.