Note that the skit is called "Buenas Noches with Diego Luca" (Spanish for Good Night/Good Evening) and is supposed to be a parody of a late-night talk shows.
I don't think Daniel Day-Lewis specifically matters much in this case. I think it could have been any other prominent figure. It seems to me that this is more of a play on "singing on motorcycles in traffic". There are some shows/bits online centered around people talking, singing, etc. in cars driving around town. The one that specifically came to my mind is Carpool Karaoke with James Corden:
Carpool Karaoke is a recurring segment on The Late Late Show with James Corden, in which host James Corden invites famous musical guests to sing along to their songs with him whilst travelling in a car driven by Corden on a planned route usually in Los Angeles, usually under the pretense of needing to get to work and preferring to use the high-occupancy carpool vehicle lane, or the pretext of needing directions from a local when in a new town, such as London (with Adele), Liverpool (with Paul McCartney), New York City (with Madonna) or Las Vegas (with Céline Dion).
(Example: Adele Carpool Karaoke)
I see this motorcycle bit as an (intentionally) bad parody of Corden's segment. First, the name is an intentionally bad rephrasing of Carpool Karaoke: singing (= karaoke) on motorcycles in traffic (= carpooling). For the bit, they cut to the host and another person (representing Day-Lewis) riding on a motorcycle, bopping their heads and singing. But they're supposed to be in traffic, on a bike instead of being in a roomy car or van, you can hear honking, and their voices are muffled through the helmets.
It's a bad bit, but the audience still cheers and applauds it. Most of the humor lies in that. However, it is also ridiculous to think that a prominent actor (such as Day-Lewis) would lower themselves to be a part of such a bit. That's another angle to it.