Final answer:
The intersex condition caused by a lack of the enzyme 5-α reductase, preventing the conversion of testosterone to DHT, is called 5-alpha reductase deficiency (5ARD), not to be confused with AIS or Klinefelter syndrome which involve different genetic abnormalities.
Step-by-step explanation:
The intersex condition described by someone with an XY chromosomal make-up who lacks the enzyme 5-α reductase and therefore cannot convert testosterone to dihydrotestosterone (DHT) is known as 5-alpha reductase deficiency (5ARD).
This deficiency prevents the proper development of external male genitalia during embryonic development, leading to a variation in sex characteristics that may not become obvious until puberty. It is distinct from conditions such as Androgen Insensitivity Syndrome (AIS) where individuals have an XY karyotype but their bodies do not respond to androgens, and Klinefelter syndrome which involves the presence of one or more extra X chromosomes in males.