Last I heard parliament has approved Brexit, actually they approved the triggering of Article 50. I don't know what has happened about the House of Lords, they have to approve the triggering of Article 50 as well and are ever more pro-EU than Parliament so I expected there to be more trouble there but I haven't heard about anything but Trump since Trump Trumped.
Parliament will have to approve the final deal as well but it's unclear whether that vote will have the option to "undo" Article 50 or if it will be a choice between whatever shit deal they eek out and leaving the EU with no deal (Theresa May probably wants the latter).
PS Just checked and it looks like the Lords are set to amend the Article 50 Bill but are expected to pass it once amended.