I think Helly lied about her overtime experience because she has come back as her outie as a mole for Lumen to get information from the innies.
Evident from her lying, also how she was so crass/defensive to Mark about Ms. Casey being not the same person as her outie. And the kicker was she had to feel around for the ON switch on the back of her computer -- unfamiliar with where it was.

I think Lumen is cloning people (clue: the sheep room) and the numbers are building the clones' emotional database. In the MDR handbook online, the number groups are WO FC DR MA (Woe, Frolic, Dread, Malice) and the numbers either make you feel afraid, anxious, happy, or angry then you bin them. What if you are coding a clone's emotional makeup (clued by the flash cut with Ms. Casey at the end of S2 Ep1 - maybe also why Ms Casey seems emotionally flat/undeveloped) Also, WHAT IF Ms. Wong is actually a clone of Ms Casey in development. That one is a stretch because they seem to be different ethnicities.

You might be right about her being a spy, but I think she lied because she was embarrassed to tell them who she really was and didn't want to deal with the questions she'd get or the fear that they'd treat her differently knowing who her dad was and what her outie was doing.

I also said to my wife, I think they're cloning people. As soon as Mark asked for his old coworkers from the board they were there the next day? I think they've cloned their bodies and put the innies conscious in them.

If they're cloning people, then I wonder if the inny/outie thing is just a cover story told to the employees. Maybe there is actually an original and a clone of each person, and the "switch" in the elevator (along with the implant) is primarily for preventing them from remembering they've been cloned.

that's a big theory and almost makes my brain hurt. BUT it would explain why Irv's outie glitch/knows the elevator to the testing floor.
Also, the newspaper is completely fabricated with their team photo put into Eisenhower ticket tape parade. Pause it and read the redacted articles too

I think her behavior towards Mark and about his wife is explained by the fact she has a romantic attraction to him.

As for lying I think she would realize that immediately makes her not one of them if they know the truth. That group is her entire world and she doesn’t want to be treated differently.

The experiment in marks basement and now he’ll get to integrate his innie and outie to find Gemma wherever she went which I wonder if she’s a clone. I also want to know the project he’s working on and what it means because cobel said he’s so close to finishing it. Irv and the door mystery seems to be coming to a head. The goat people and is that cloning as well and why were there so many employees in that department. Who the man was Cobel was scared of. Milchek rejecting the paintings. Just so many storylines I wish this all came out at once.

1. I concur with the thought that Helly R is posing as an innie - though I don't know why since all their conversations appear to be recorded. The other reason for her off-ness could be the romantic thing, and I think outie Helena was intrigued by that kiss as well.
2. I think Lumon has control over the outie as well as the innie. I guess both are classified as Lumon employees. The ability to get them all back to the severed floor by offering a pineapple gift basket points to switches in the outies that can be activated. Selvig asks if a pineapple was involved. When an employee is severed, the company has control over both entities. The theme of Evil Industry exerting mind control over the populace.
3. The Keir cult worship is creepy AF. It doesn't appear non Lumon employees are even aware of the cult the innies are immersed in. Perhaps it is a control tool for the severed who have a child-like emotional level - or a mechanism for full emotional control.
4. Rikken is a hoot.

On 1, I think it makes sense she would want to go down as herself after her innie tried to kill her and sabotage her entire company. Plus as you said, I think she's intrigued at why her innie kissed Mark.

On 2, I agree and disagree. On the pineapple thing, I took that as more of a sign that Cobel was saying that Mark wasn't important and everything they do is extremely calculated. The gift wasn't a true apology or anything like that, it was a standard calculated decision by the company.
On the other hand, I think there is definitely control going on but in a different way. Watching Dylan G in this episode, I think they are grooming his innie to take over his outie completely. I think his wife is annoyed with his outie as being lazy and unhelpful, but his innie is motivated and "better". That's why she lies as to how it went. And once they offer his innie this opportunity, then Lumen controls him forever because they can always "kill" his innie at any time. Dylan G will become a company man for life. It wouldn't surprise me if several other characters like Cobel and Milchek have already had this happen.