As TMZ first reported, Myla was in a boyfriend/girlfriend relationship with Kris since mid-January -- something Kris was desperately trying to hide ... to the point his people lied about the relationship.

As for why Kris wanted to cover it up ... sources tell us Kris and his lawyer were worried it would have an impact on the divorce case. We know Kris demanded $7 million from Kim, claiming she devastated him by filing divorce papers. It's hard to say he was devastated when he moved on two months after divorce docs were filed.

Sources say Kim's lawyer wants to know if Kris said anything about his marriage which might relate to his claim Kim defrauded him -- in other words, did he blow his cover during pillow talk. We're told Kim's lawyer also wants details about hundreds of texts and emails exchanged between Myla and Kris.