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Editor: Lane, of all the days in the calendar,
you picked this one to shift into slo-mo.

Lois: Keep your pants on. l'm almost done.
l need a couple more milliseconds.

Editor: You snooze, you lose. He won't tolerate slow working?
Larkin has submitted his piece. His version of the article?
l'm running it as tomorrow's headline. He'll print his piece and not Lois'?
Might wanna try a typing class, give you a leg-up. Boost?

Chloe: Why do l get the suspicion that you two
have had the Dear John conversation? Private conversation?

Lois: Yes, we sure have. And let me tell you, those conversations
tend to quickly veer into awkward territory.

Chloe: You think he'd be man enough to suck it up... Do you believe
he'll have the guts to come to his senses?
and treat you like everyone else.

Lois: Yeah, you'd think so. I believe so?
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MadhulkEditor: Lane, of all the days in the calendar,
you picked this one to shift into slo-mo.

Lois: Keep your pants on. l'm almost done.
l need a couple more milliseconds.

Editor: You snooze, you lose. He won't tolerate slow working? okay
Larkin has submitted his piece. His version of the article? Perhaps
l'm running it as tomorrow's headline. He'll print his piece and not Lois'? Perhaps

You must know something I don't. (prior context?)
There's not enough here to reach that conclusion.
Larkin's piece may or may not be on the same subject,
and may or may not replace Lois' version.

Might wanna try a typing class, give you a leg-up. Boost? Yes - a hand - sometimes, an advantage over others.

Chloe: Why do l get the suspicion that you two (what two?)
have had the Dear John conversation? Private conversation? No. This was originally the nick-name for a girl back home informing a soldier in the war that she'd found somebody else. (She sent him a "Dear John" letter, or just a "Dear John.")

Lois: Yes, we sure have. And let me tell you, those conversations
tend to quickly veer into awkward territory.

Chloe: You think he'd be man enough to suck it up... Do you believe (You'd think?)

he'll have the guts to come to his senses? (take it like a man - something like that)
and treat you like everyone else.
(Like everyone else treats you - or like he treats everyone else?)

Lois: Yeah, you'd think so. I believe so? (One would believe that under the circumstances, that's what he should do.)

Comments  
Students: Are you brave enough to let our tutors analyse your pronunciation?
MadhulkEditor: You snooze, you lose. He won't tolerate slow working?

Yes.
MadhulkLarkin has submitted his piece. His version of the article?
"piece" = the story he has written (not necessarily his version of the article Lois has been working on, though it could be if that fits the context)
Madhulkl'm running it as tomorrow's headline. He'll print his piece and not Lois'?
He'll print Larkin's story on the front page. He doesn't explicitly say he won't print Lois' story, but you could infer that.
MadhulkMight wanna try a typing class, give you a leg-up. Boost?
Yes.
MadhulkDear John conversation? Private conversation?
Conversation in which one partner in a (romantic) relationship tells the other that the relationship is over.
Madhulk
You think he'd be man enough to suck it up... Do you believe

he'll have the guts to come to his senses


I think "you" here means "you would", meaning "people generally would think this" or "it's a reasonable thing to believe".

"he'd be man enough to suck it up" = he'd be mature/strong enough to get over it (the breakup, I assume) and get on with "business as usual" at the office.
Madhulkyou'd think so. I believe so?
It would be reasonable to think this.
Thank you Avangi and Mr Wordy!