Can a lay person become an Arahant according to the Suttas?

One of the Dhammapada stories (for example) suggests it's possible.

Dhammapada Verse 142 – Santati Mahamatta Vatthu

In agony, he tried to think of a refuge and remembered the Buddha. He went to the Buddha, accompanied by his followers, and related to him about the grief and anguish he suffered on account of the sudden death of the dancer. He then said to the Buddha, "Venerable Sir! Please help me get over my sorrow; be my refuge, and let me have the peace of mind." To him the Buddha replied,

"Rest assured my son, you have come to one, who could help you, One who could be a constant solace to you and who will be your refuge. The tears you have shed due to the death of this dancer throughout the round of rebirths is more than the waters of all the oceans."

The Buddha then instructed the minister in verse. The meaning of the verse is as follows.

"In the past there has been in you clinging (upadana) due to craving; get rid of it. In future, do not let such clinging occur in you. Do not also harbour any clinging in the present; by not having any clinging, craving and passion will be calmed in you and you will realize Nibbana."

After hearing the verse, the minister attained arahatship. Then, realizing that his life span was at an end, he said to the Buddha, "Venerable Sir! Let me now realize parinibbana, for my time has come."

I think that counts as Theravada: apparently the stories were compiled 5th century CE, by Buddhaghosa who is called Theravadin.

Other things to note:

• It was deep distress, sorrow, grief (perhaps disenchantment) that led to his seeking refuge. My guess is that at that point in his life perhaps he found that his clinging was no longer tenable, perhaps he then no longer had the attachments you'd expect to find in a lay person.

• His having attained arahatship, perhaps you would no longer call him a lay person.

  At the congregation, the bhikkhus asked the Buddha, "Venerable Sir! The minister had realized parinibbana dressed in full regalia; is he a samana on a brahmana?" To them, the Buddha replied "Bhikkhus! My son can be called both a samana and a brahmana."

  Then the Buddha spoke in verse as follows:

  Verse 142: Though he is gaily decked, if he is calm, free from moral defilements, and has his senses controlled, if he is established in Magga Insight, if he is pure and has laid aside enmity (lit., weapons) towards all beings, he indeed is a brahmana, a samana, and a bhikkhu.

This version of the story explains that Santati had been the follower of Vipassī Buddha in an earlier kalpa, had preached the Dhamma for eighty four thousand years ... perhaps that (i.e. his past life) helps to justify why he might be called "a brahmana, a samana, and a bhikkhu".

Thus have I heard: A lay person can become an Arahath, but he will enter the Sangha within a week or he will enter Parinibbana. If it's a Pacceca Buddha, he will leave the lay life to dwell in the forest since there's no Sasana in the world. Also, if an Anagami lay person dies, he will be born in one of the pure abodes. There he will attain Arahantship and won't be entering the Sangha.

The answer is Yes. Please look through this website.

"If a layman attains arahant-ship, only two destinations await him; either he must enter the Order that very day or else he must attain parinibbàna" -- Milindapanha III.19

This is what one of the suttas says:

When this was said, the wanderer Vacchagotta asked the Blessed One: “Master Gotama, is there any householder who, without abandoning the fetter of householdership, on the dissolution of the body has made an end of suffering?”¹

“Vaccha, there is no householder who, without abandoning the fetter of householdership, on the dissolution of the body has made an end of suffering.”

“Master Gotama, is there any householder who, without abandoning the fetter of householdership, on the dissolution of the body has gone to heaven?”

“Vaccha, there are not only one hundred or two or three or four or five hundred, but far more householders who, without abandoning the fetter of householdership, on the dissolution of the body have gone to heaven.”
-MN 71, To Vacchagotta on theThreefold True Knowledge (Tevijjavaccha-suttaṃ)

¹ (Post-canonical texts:) MA explains “the fetter of householdership” (gihisamyojana) as attachment to the requisites of a householder, which MT details as land, ornaments, wealth, grain, etc. MA says that even though the texts mention some individuals who attained arahantship as laymen, by the path of arahantship they destroyed all attachment to worldly things and thus either went forth as monks or passed away immediately after their attainment. The question of lay arahants is discussed at Miln 264.

^{Disclaimer: Taking only this discourse into account (without post-canonical works), the following is what I find reasonable. If there are other suttas which also shed light on this, I'd be glad to know.}

So, it seems a householder cannot make an end to suffering on the dissolution of the body without being free of the "fetter of householder-ship". Since this applies to the furthest case of "on the dissolution of the body", it would be safe to assume that it also applies before. If this is correct then the answer depends on the meaning of "householder" & "fetter of householder-ship". Since the meaning of "fetter of householder-ship" is not, as far as I know, explicit in any of the discourses, I'll lay out two cases:

Case 1
If "householder" means "living in a house" & "fetter of householder-ship" means "owning a house"
Then, the answer is yes, since one can live in a house without being it's owner.

Case 2
If "householder" & "fetter of householder-ship" mean the same thing as "living in a house", Then, the answer is no, since the problem is living in a house.

Since Case 2 seems absurd (because of it's implications) and Case 1 is suggested implicitly by the possibility of there being householders who -have- abandoned the "fetter of householder-ship", I would say:

"Yes, a lay person -without- the fetter of householder-ship can become an arahat".

I hope this is understandable & helpful.