As a UK-born native English speaker I don't recognise the phrase
lazy common sense
as an established idiom, however I think it is possible to deduce the meaning.
We frequently use phrases such as
it's just common sense
implying that something is self-evidently true and needs no further justification. Adding the word lazy is clearly intended to imply that further thought is needed, that the common sense is actually, if not wrong, then at the very least not self-evidently correct.
So we might read this as
it is a widely-held belief that ... but we should consider that ...
I might have used instead
Received wisdom ...
implying that the concepts have been passed from person to person, perhaps from generation to generation and should be more critically examined before being accepted as true.