Today's Losties are the first whose connection comes entirely from the limited perspective of the relatively short season 4: Daniel Faraday and Kate Austen; an Oxford professor and an Iowa girl who we're not even entirely sure graduated from high school; a guy who wears his skinny tie with pride in a jungle, and Little Miss Facesmear. This connection is all about the new parallel between how our Losties basically appear to the new Freighter arrivals much the way the formerly mysterious Others once appeared to our Losties, I think. Kate is a savvy tracker Jungle Gal type, and Faraday is... the complete opposite.
Daniel Faraday's arrival on the Island (in The Beginning of the End) is anticipated by the optimistic among our Losties as something just shy of the Second Coming of Our Lord and Savior, Jesus Christ the Nazarene. Jack and Kate are reminiscing about poor, dead Charlie while at the cockpit when they hear the sound of Frank's helicopter above, sounding in bad shape, and see a blinking light coming down nearby. They head in that direction, and are on the scene to get their glimpse of what will become a familiar sight: Daniel Faraday stumbling around and looking completely hapless and out of place in the dangers of the Island jungle. Look up "fish out of water" in a TV/Movie glossary, and Daniel Faraday will be right in there, along with Borat, City Slickers, Coming to America, and you know, Darryl Hannah's literally fish-out-of-water mermaid from Splash. Oh, Faraday, you're so adorably academic. Kate has the same look on her face as when she discovered the Apollo candy bars in early season 2 when Daniel asks, "Are you Jack?"
Announcing that he is there to rescue them, Faraday starts to stumble out what he could do if he had his phone, which is in his missing pack, when Kate offers that they have a phone (Naomi's). Faraday is somehow surprised to hear this, even though he knows that Jack called the Freighter on that same phone, hence how he knew Jack's name. I don't think this is so much a continuity error as an example of how Faraday's mind is so constantly up in the scientific stratosphere and not thinking through very common sense logic. He's a bit of a goof, really.
Following the signal on the phone towards Miles, the trio finds a box from the helicopter containing an ominous-looking gas mask, and Jack asks Daniel why he's packing heat, which leads to the infamous line about rescuing the Losties not being their "primary objective." The tension continues to heat up when they find Miles and he accuses Kate of killing Naomi. This leads to Daniel making a very curious statement about Jack and Kate to Miles: "these are good people."
Now, that might seem like a throwaway line to the casual viewer, but LOST fans should recall that the phrase "good people" is one of those big mythology tag lines that the Others, mostly, threw around a lot in seasons 2 and 3. What we don't know yet is what the Others really meant by "good people", and what significance such standing has with The Island. And for that matter, are Jack and Kate actually good people, inasmuch as The Island defines that term? In other words, is this Daniel just saying something in a context he doesn't truly understand, or does he somehow in fact know what's saying about them (whatever that might be, which we don't really know at this point)?
While Miles communes with Naomi's corpse, Miles is mildly freaking out, talking about how the light doesn't scatter quite right on the Island. Kate tries to bring him back to Earth (good luck with that, Freckles), saying that he doesn't need the gun because, you know, Kate and Jack are such awesomely good people. Remember that? Daniel says Miles would kill him. And then talk to his corpse, probably. When their newly large group (with the addition of Sayid and Juliet) arrives at the helicopter, Kate and Daniel team up to load Naomi's body onto it, which annoys Miles to no end, saying that her body is "just meat." Soon after, Kate goes off with Sayid and Miles to the Barracks on their mission, so that ends her interaction with Daniel for a while.
After some quality sexy time with Sawyer that is brought to a screeching halt by his delight that Kate wasn't pregnant (he even did a "Woo !"), Kate headed back in the direction of the Beach camp and Jack, who would never ever "Woo !" about her lack of imminent motherhood. And on the way there, Kate came across... Daniel and Charlotte, on their way to execute some sort of sinister plan at the mysterious Tempest Station. There is some awkward lying and cat and mouse logic between Daniel and Kate (who Charlotte is pointing her gun at), which goes a long way to demonstrate what an awful, awful liar Daniel is. If you have a secret, don't tell the fat guy... or the egghead. Kate spots their gas masks, which lands her a nice big lump on the head courtesy of C.S. Lewis.
After all the drama of the affair at Ye Olde Tempest Station, Daniel and Charlotte return to the relative domesticity of the Beach Camp, and sort of settle in. From this point, on the narrative between Daniel and Kate sort of slows down to a trickle, and not a particularly interesting one. There's drama at the Beach about the Freighter, and Jack's appendix problem, and lies about the radio, but Kate and Daniel don't have the same sort of "she's good people" bond anymore. And then Kate gets her helicopter ticket to become one of the Oceanic Six while Daniel is busing ferrying future dead redshirts to the Freighter, and that's pretty much it for this connection. Kate's off in the future, no longer being a Jungle Gal, and Daniel will presumably be back on the Island soon, being perplexed by jungle dust and moonbeams. Any imminent Daniel/Kate interaction is very unlikely, probably until season six, if Daniel isn't Smokey bait by then.