They can be lay arahant, but classical Theravada just say they cannot live for too long.
You mean to ask why they cannot live for too long?
The life of a lay person has not enough virtue/precepts to contain the pure mind of an arahant.
Arahants do not long for death or life, without desire, they don’t work (for money), they might not eat. Non returners it seems already don’t use money.
Maybe when ordained, even as a sāmaṇera (as there were kid arahants), out of respect for the Buddha, dhamma and saṅgha, they go for alms arounds and eat and thus continue to survive.
I had heard that one way to verify authentic Bhikkhuni ordination is to see if an arahant bhikkhuni would live long. I think perhaps people forgot that there were sāmaṇera arahants. So it could be in general that a recluse lifestyle which is more of the factor to increase lifespan of lay arahant.
Certainly, it’s not too hard for a dedicated lay people to set up conditions so that they can live with 8 precepts or more. Anagārika/Postulants (similar to samanera, but in white robes) in SBS are not strictly speaking a part of the 5 saṅgha (Bhikkhu, Bhikkhuni, Sāmaṇera, sikkhamāna, sāmaṇerī), but could be enough. And many other semi monastic styles which cropped up in modern times. Including Sayalays or Mea Chees.