Back in Cuddy's office, House asks if he can have a minute alone with his "future former employee." They go outside to the patio Cuddy apparently has connected to her office, where House asks Chase why he lied to Sam about being hung-over so that Sam would sue PPTH. He knows that Chase wasn't hung-over that day; House would have fired him back then if he thought he was. So drinking too much gets you fired, but a freaking meth hangover is okay? Chase doesn't think it matters whether he was hung-over or not; Kayla's still dead and it's his fault. At least now Sam will get all the money he'll need to take care of Kayla's daughters. House says he knows what was really wrong with Chase that day. He's pretty sure who called Chase before Kayla walked in, and why.
Back in the past, Chase gets his phone call. His expression changes from confusion to shock as he listens to the other end. "What did he die of?" he asks. Pause. "That's impossible. I saw him two months ago. If he had lung cancer he would've --" and then his stepmother apparently tells him that his father didn't want to tell him about the cancer. Numb, Chase starts to put the phone down. Kayla walks in.
House says he's figuring that, now that both of Chase's parents are dead, the chances of a grief-over-parental-death-related mistake not happening again are pretty good. It then occurs to Chase that House shouldn't have had any reason to think that Chase was distracted because his dad died. Except for the fact that Chase the Elder was supposed to be a world-famous doctor whose death would, I'd assume, be widely reported in the medical community. House sighs and admits that Chase the Elder told House about the cancer and asked House not to tell Chase. Chase is kinda pissed that House "hung [him] out there to be blindsided," and it's probably House's guilt over that that's the reason he didn't fire Chase in the first place. House tells Chase that he can either tell the committee about his dad, which will let him keep his job and still give Kayla's family enough money to keep their house, or Chase can keep lying and lose his job. Just like he did with Chase's dad, House will keep his mouth shut about the truth, even though, as he points out, it's much better for House legally if Chase lies. I think he only said that because he figured Chase would be mad enough at House to tell the truth just to get House in more trouble.