There is a rich hyperbolic linguistic tradition in the Semitic languages (indeed, in the Arabic generally), and I think this is just one instance.
The story of the small gate is largely dismissed today as there being no evidence to support it, but then much of what Luke said in his Gospel suffered the same fate until archaeological evidence showed scholarly assumptions to be wrong. Indeed the existence of the pool of Siloam, spoken of in John's Gospel, was denied, and this argument was used to refute the eye witness veracity of John's testimony — until it was discovered!
Most walled structures had what was later called a 'sally port' — a small and often concealed door that messengers or even raiding parties could slip in and out of, so this one should not be written off.
Having said that however, remember Jesus also spoke of a plank in one's eye, and again, of the 'mustard tree' which would seem to be as big as an oak, but in fact never grows very big at all.
And Luke's Greek for 'needle' refers to a surgeon's needle specifically, but then, Luke was a bit of a doctor ...
On the other hand we have:
"They do not show a man a palm tree of gold, nor an elephant going through the eye of a needle."
Babylonian Talmud, Berakoth, 55b
"… who can make an elephant pass through the eye of a needle."
Babylonian Talmud, Baba Mezi'a, 38b
"A needle's eye is not too narrow for two friends, but the world is not wide enough for two enemies"
Source not traced but cf. Midrash Rabbah, Genesis 1.3
"The Holy One said, open for me a door as big as a needle's eye and I will open for you a door through which may enter tents and [camels?]"
Midrash Rabbah, The Song of Songs, 5.3; cf. Pesiqta R., 15, ed. Friedmann, p.70a; Soncino Zohar, Vayikra 3, p95a
As Wil said, the Lamsa Bible was a retro-translation, so not really very useful at all, and his argument rested on a mistranslation of the Greek for 'rope' (kamilos) as 'camel' (kamelos) — but the oldest texts we have use the word 'camel' not 'rope'.
Of all, I delight in the last text cited above ... if the sinner opens just the slightest 'needle's eye' of an acceptance of God, then God will open up the gates of heaven for him.
God bless,
Thomas