His tribute to George Carlin, where he discussed how George inspired the direction his material took, is incredibly heartfelt.
You can tell too, that he started rushing through the final bits of his speech because he was barely holding back tears.
Him welling up while talking about the birth of his daughter on his WTF Podcast interview. Despite what he says about them on stage, he really, really loves his kids.
Further exemplified when he appeared in Jerry Seinfeld's web series Comedians in Cars Getting Coffee, where Louis recounted his attempts to take his daughters on a boating trip (with the story playing out in animated format for the viewers). The trip goes sourly, with the trio caught on shore in quicksand for roughly 12 hours before getting pulled out by the coast guard. It's clear that Louis feels terrible for the negative turn of events, and in the aftermath, he tells his daughters that they have to go again one day so they can have a really good experience. To this, his daughters (at least one of them) respond by saying "We DID have a really good experience", making this a Crowning Moment all around.
His introduction to the "Best Documentary Short" award at the 2016 Academy Awards, where despite all the jokes he gave a clearly sincere speech about how it's his favorite Oscar of all, since it gives attention to several films that badly need it every year, and every single award makes a genuine difference in the winner's life.