Parable, fable, story, simile et al are all synonymous, and parables aren't exclusive to the Bible. You're arguing over semantics, while not providing what's supposed to be the correct term.
All 6 ECF who quoted/referred to the story Lazarus and the rich man, as factual.
[1]• Irenaeus Against Heresies Book II Chapter XXXIV.-Souls Can Be Recognised in the Separate State, and are Immortal Although They Once Had a Beginning.
Ireneaeus, [120-202 AD], was a student of Polycarp, who was a student of John.
1. The Lord has taught with very great fulness, that souls not only continue to exist, not by passing from body to body, but that they preserve the same form [in their separate state] as the body had to which they were adapted, and that they remember the deeds which they did in this state of existence, and from which they have now ceased,-in that narrative which is recorded respecting the rich man and that Lazarus who found repose in the bosom of Abraham. In this account He states that Dives [=Latin for rich] knew Lazarus after death, and Abraham in like manner, and that each one of these persons continued in his own proper position, and that [Dives] requested Lazarus to be sent to relieve him-[Lazarus], on whom he did not [[formerly]] bestow even the crumbs [[which fell]] from his table.
[2]•Clement of Alexandria [A.D. 153-193-217] The Instructor [Paedagogus] Book 1
On the Resurrection.
This was the day. “And a certain poor man named Lazarus was laid at the rich man’s gate, full of sores, desiring to be filled with the crumbs which fell from the rich man’s table.” This is the grass. Well, the rich man was punished in Hades, being made partaker of the fire; while the other flourished again in the Father’s bosom.
[3]•Tertullian IX A Treatise On The Soul Chap. VII [A.D. 145-220.]
In hell the soul of a certain man is in torment, punished in flames, suffering excruciating thirst, and imploring from the finger of a happier soul, for his tongue, the solace of a drop of water. Do you suppose that this end of the blessed poor man and the miserable rich man is only imaginary? Then why the name of Lazarus in this narrative, if the circumstance is not in (the category of) a real occurrence? But even if it is to be regarded as imaginary, it will still be a testimony to truth and reality . For unless the soul possessed corporeality, the image of a soul could not possibly contain a finger of a bodily substance; nor would the Scripture feign a statement about the limbs of a body, if these had no existence.
[4]•Tertullian Part First A Treatise On The Soul Chapter 57
9. Moreover, the fact that Hades is not in any case opened for (the escape of) any soul , has been firmly established by the Lord in the person of Abraham, in His representation of the poor man at rest and the rich man in torment.
[5]•The Epistles Of Cyprian [A.D. 200-258] Epistle 54 To Cornelius, Concerning Fortunatus And Felicissimus, Or Against The Heretics
Whence also that rich sinner who implores help from Lazarus, then laid in Abraham’s bosom, and established in a place of comfort, while he, writhing in torments, is consumed by the heats of burning flame, suffers most punishment of all parts of his body in his mouth and his tongue, because doubtless in his mouth and his tongue he had most sinned.
[6]•Methodius . [A.D. 260-312] XIX he Discourse on the Resurrection. Part III. [A.D. 260-312]
But souls, being rational bodies, are arranged by the Maker and Father of all things into members which are visible to reason, having received this impression. Whence, also, in Hades, as in the case of Lazarus and the rich man, they are spoken of as having a tongue, and a finger, and the other members; not as though they had with them another invisible body, but that the souls themselves, naturally, when entirely stripped of their covering, are such according to their essence.
