They are both correct and used even among journalists.

Incorrect.

"A lede is the introductory section in journalism and thus to bury the lede refers to hiding the most important and relevant pieces of a story within other distracting information."

Burying the lead in the journalism would actually be burying the lead (like the metal) so they aren't even pronounced the same. Many people make the same mistake you do so this misconception proliferates.

My phone corrects my spelling. Lately it has begun correcting my grammar. How long until it points out idiom misuse?