Except depending on the country is it more complex than that. Components may belong to Hololive, but the same could be said about Dr. Seuss Enterprises and the music creator.
This level of ambiguity are why courts exist.
Though likely, Cover will settle and ban the talents from singing the song. Likewise, Holobass will likely only be able to sell the karoke(IE instrumental) version and may need to pay Dr. Seuss Enterprises royalties/legal fees for using their lyrics if he made any money off of the lyric version. Hell, even trying to make money off of Dr. Seuess' Enterprises lyrics might be enough for them to collect if they so choose to pursue.