Colloquial and northern-flavored. 愣 (lèng) on its own means 'stunned/dumbfounded', but in the adverbial slot here it carries a stubborn-against-reason flavor — 'flatly insist on something obviously untrue'.
mistakes
Don't confuse with 楞 (the variant character) or with 冷说 — the 愣 here is fourth tone (lèng), not the second-tone 楞 some learners default to.