Ilana takes ashes where Jacob burned + Ben lies about killing him

At the four-toed statue, Ilana is sitting inside crying when Ben enters. She asks him what happened to Bram and the rest of her team. Ben tells her that Locke turned into a pillar of black smoke and killed them, but he lies and tells her that Locke killed Jacob too. When he tells Ilana that Jacob was kicked into the fire, she goes to the pit and scoops out a handful of ashes and puts them in a small pouch, much like the one Bram had. When Ben asks why Locke carried Richard into the jungle, Ilana says that he's recruiting.

So what exactly is Ilana's connection to Jacob? She not only seems concerned, but emotionally devastated by his death.