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.