Final answer:
Merv Griffin composed the theme song 'A Time for Tony' for his son and used it as the theme song for 'Jeopardy!', earning him millions in royalties.
Step-by-step explanation:
The TV show for which Merv Griffin used his lullaby as the theme song was 'Jeopardy!'
'Jeopardy!' is a popular game show that debuted in 1964 and is still on the air today. The show's theme song, titled 'Think', was originally composed by Merv Griffin as 'A Time for Tony'. The decision to use this lullaby as the theme song proved to be very lucrative for Merv Griffin, earning him an estimated $70 million in royalties over the years.
Griffin composed numerous other theme songs in addition to 'A Time for Tony', including 'Wheel of Fortune' and 'The Littlest Hobo theme'.