Do you have any ideas of what an interaction between Connor and Lindsey would look like?
God I think it would depend on the iteration of the characters we're talking about. I do think there's a universe where Lilah and Lindsey are fully Team Rocket and baby Connor is their Pikachu. I also think there's a universe where Lindsey decides he's Connor's godparent without anyone asking, shows up to parent-teacher conference night uninvited, gets into a public argument with Angel, and the teachers have to reassure them that they've worked with non-traditional families before, do you and your ex-husband share custody, etc.
But most realistically in canon s5 I think if Lindsey somehow found out that Connor was Angel's kid, he'd try to manipulate him like Holtz did, except Connor would be 17 and well-adjusted and think Lindsey was lame. Actually given the wackiness of Lindsey and Eve's schemes in s5 anyways, I can see him going undercover as a guidance counselor at Connor's school and trying to turn him to the dark side, only he keeps getting bullied by a bunch of teens who can smell his inferiority complex. He can get a subplot where he has to counsel a troubled teen girl who's been acting out because her ex-boyfriend dumped her and became homecoming king/queen with another girl, and it's not fair that HE gets everything SHE wanted, and Lindsey is nodding along like, Absolutely. You deserved that title. That bastard used you and left you for dead and now he's getting rewarded for it? I'll bring the shovel.
And then they do some wacky hijinks to get supernatural revenge on her ex-boyfriend, except at one point Lindsey has a blinding moment of self-awareness as he realizes he's playing co-conspirator to a literal teenager over petty high school drama, and it gives him pause just long enough for Angel to show up because he's investigating a lead on demon activity at Connor's high school. Angel asks what he's doing and all that self-awareness disappears as Lindsey must now double down on why his plan to defeat Angel his teenage mentee's plan to get back at her ex-boyfriend definitely makes sense and is a good idea, actually.
the Illyriad Wesley has been living in my brain rent free, so please take this as an offering. This AU was created by @genericaces I believe! Their art is absolutely amazing and feeds the brainrot I have for the whole Angel Investigations crew.
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God okay I have normal thoughts on this ship. The short answer is that I don't think they should get together, because I think the best case scenario (or rather, the most narratively satisfying scenario to me personally) for Lindsey is moving on from Angel and getting a life, and I also believe Angel genuinely does not care for him. I say this as someone who enjoys both characters too much for my own good.
However I DID psych myself into thinking through the circumstances in which they would fuck, which I won't regurgitate but you can read through my initial rant here.
The TLDR/followup to that is that I can only see them getting together in a situationship that brings out the worst in both of them, ultimately bringing them to an impasse where they're forced to change and deal with their repressed inner conflicts lest they implode. The relationship ends up being necessary for their respective character growth but is ultimately doomed and needs to end for their arcs to conclude.
(Also I always feel bad when I say I'm not necessarily interested in a ship as romantic/endgame, but most of the time it's because I'm abnormally attached to some other, weirder idea for what their relationship could be. Which is all to clarify that I'm coming at this from a place of love.)