Hi! So I'm not 100% sure if we're thinking about the same post, but if so I think I might've replied to it at some point. And disclaimer before I say anything: many interpretations are valid, and one of my favourite things about this arc is that it introduces so much complexity.
Personally, I think he's talking about Declan. Not because of any particular character thing about Emily - just because it makes narrative sense. The entire arc is this slow unveiling of what he is actually getting revenge for, and it's Declan. So from memory here's kind of how the 'reveal' of Declan goes. I am definitely going to miss things.
- "You took the only thing that matters to me." - we have no idea what he's talking about here, just that whatever it is, he wants Emily to pay with her life.
- "Happy birthday, my love." - again, we don't know who he's talking to, but he's in a Catholic church lighting a candle at a side altar so they're probably dead.
- The whole reveal about the gimmel ring and the flashback to him giving it to her - we learn they were in a committed relationship and that he wanted to marry her. (This is another place the fandom differs but it's at least complicated for her, and he does seem to genuinely love her in his own fucked up way.)
- Some members of the team are used narratively to try to plant the idea with the audience that maybe this ruthlessness actually does say something Bad about Emily. Whether you think this is clumsily done or a logical place for Morgan's mind to go is up for interpretation, but the things he says are there in the script to plant the question 'is she bad, actually?'
- "This won't be the first time you've killed an innocent, but it will be the first time you have to watch". We're like 'omg what is he talking about', because we still don't know about Declan. [[From his POV, as far as he knows, she was the only person who knew about his son, and his son was killed by someone else to break him. She caused his son's death, but didn't have to watch. It just feels overwhelmingly more likely that this is what he's referring to here than anything else, because getting her to confess to this is the entire point of capturing her and torturing her.]]
- That weird hammy scene between Rossi and Ashley where Ashley is like "WHY FAMILIES???" that leads to the team realising Doyle killing a child he could've chosen to spare could be the key to figuring out why he's taken Emily. Clyde wonders, if Doyle had a kid, why Emily would've kept that from him, and we don't know the answer.
- Doyle tells Emily if she knew where to find him she knows "what this is about", and it's time for her last confession. She says "take me to where he died" - this is the first time we hear her acknowledge Declan at all and it's like 15ish mins from the end of Lauren.
- The flashback of her with Declan. She clearly loves this kid and cares about protecting him. Uh oh did she actually get this child killed????
- Doyle shows her the photo of Louise and Declan. They very much appear to be dead, she is the only person who knew Declan was his child, she admits to putting him in the profile and Doyle says the photos were what broke him and got him to talk. She's crying about it. It very much seems like this child is dead and she is responsible. (I honestly think as long time fans and people obsessed with this arc, we forget how late this reveal comes and how much the audience does not know what really happened yet at this point.)
- "There's something you don't know about those photos" etc etc etc where we hear Emily fill in what Doyle (and the audience) didn't already know, and makes her behaviour fit with what we already knew about her - she put a lot on the line to protect this kid, even kept him a secret from Clyde, who has been established as Even Shadier Than Her, and all is well with our understanding of our ruthless fave.
Narratively, almost every single thing Doyle says to or about Emily is slowly revealing to the audience what he understands of what happened to his son, and then from 'there's something you don't know about those photos', it's Emily telling us what Doyle didn't know. It doesn't really make any sense (to me) for this one thing to be totally unrelated to that, especially for him to choose this particular moment to not to make it about Declan. Fahey isn't a stranger - Ian is about to have her choose the life of one innocent person she knows over another. As far as he knows at this point, she bonded with his kid and then had him killed as a means to her own end. Pointing a gun at two friends and an acquaintance and making her choose who to kill is the perfect moment to torture her with that fucked up choice he fully believes she already made.
I think with hindsight, looking back when we already know the whole story, it's easy enough to spin it another way. But in the context of this whole arc being a slow unveiling of Declan, it just doesn't make any sense to me for that to be an unrelated statement about some other shady thing she did, because all Doyle cares about is getting revenge for her getting Declan killed.
(That said, I think Emily is a pretty morally grey character, and I always think about what Reid says about the undercover cop in Retaliation - "good guy doing bad things". I'm sure Lauren did plenty of bad things because you need to if you're not going to blow your Bad Guy cover. I think Ian does that fond 'hello, Lauren' when she says to shoot Fahey not because he's familiar with her making the choice to kill someone, but because he's familiar with the ruthless logic she uses, and the way she protects the people closest to her first. It's very Emily, and apparently very Lauren too.)