Who is mighty Constantine or Lucifer?

Did the "Hellblazer" Constantine ever meet Lucifer?

In the 2005 film "Constantine", the main character has a little tête-à-tête with the Devil, aka Lucifer Morningstar, at the climax of the film.

But in the Vertigo comic universe, Lucifer quit the job:

He grew tired of the various stereotypes and prejudices that mortals held of him, such as the idea that he was buying souls for souls that were largely untrue and forcing mortals to commit evil deeds. He was fed up with his rule over Hell and found it an unfair punishment that he had to rule there forever just because he rebelled once.

His job was taken over by the First of the Fallen, who is much older than old Luc, who rules along with the Second and Third of the Fallen (until he realized he is much more powerful than them) and he, usually not Morningstar's main antagonist John Constantine.

Did Constantine ever meet the original devil?

Edit from Wikipedia

Constantine also makes a small cameo in Vertigo's Lucifer. In issue no. 5 he drinks in the Bar Lux by Lucifer Morningstar among guests who, with Lucifer, are looking for an audience through the gateway to the void outside of creation. He himself is not there to propose a deal with Lucifer just to "take a quick look at the field". [41] Lucifer Morningstar returns in Hellblazer # 192. Lucifer writer Mike Carey wrote Hellblazer between issues 175–215.

JohnP

Part of New 52, ​​I ... Vampire # 19, I think he does. (At least the wiki is ideal for this).

JoJo

John went into his bar somewhere on a single page in Lucifer # 5; and once he mentions the morning star in the city of demons.

Rand al'Thor ♦

Welcome to Stack Exchange! Maybe you could add some quotations to this answer (e.g. when is John already gone to his bar)?