The most appropriate option to fill in the blank is late.
Late means near the end of something. It is the most appropriate word to fill in the blank because it describes the fact that the man was in his thirties, which is near the end of the age range for being considered young.
Lest means in order to avoid something. It does not make sense in the context of the sentence.
Latter means the second of two things mentioned. It does not make sense in the context of the sentence.
Least means the smallest amount or degree. It does not make sense in the context of the sentence.