Confusingly, 好不热闹 and 好热闹 mean the SAME thing, both mean 'very lively'. The 不 is rhetorical and actually intensifies rather than negates. However, 好不容易 means 'with great difficulty' (not easy at all).
grammar
好不 + adjective = extremely/very (rhetorical emphasis). This is a classical Chinese survival where 不 strengthens the meaning. Context determines whether it negates or emphasizes.
