I would read them in that order. The endings are nice and complimentary too. I think McCarthy read Lebowitz and took some inspiration. Lebowitz is also a good palette cleanser after the tender bleakness of the Road. Intellectually stimulating and different enough while in my mind being a non cannon sequel to the Road. Love both books so much. Good little post apocalypse pairing
You could try reading “On The Beach” then “The Road” then “A Canticle For Leibowitz”. Save the best for last.
Glad I made this post. So many cool recommendations!