In Mormonism, how is the doctrine of Adam & Eve inability to have children prior to the Fall explained?

First, Adam and Eve were also waiting for further light and Knowledge When Lucifer came tempting. We don't know what would have been provided.

Second, Lucifer was out of line for giving them the fruit using the excuse that he was only doing what was done elsewhere. It was not his place to do it. But it may be inferred that it was normal and expected for the fruit to be given at an an appropriate time by someone authorized to give it.

What if they would have eventually been given the fruit with proper preparation at the right time by an authorized party rather than yielding to temptation?

This question deserves a more in-depth answer, but first, let me get something out of the way.

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I posted an answer to Are “sin” and “transgression” different in LDS terminology? that contradicts the regrettably popular opinion that sin and transgression are different. Various Church leaders over time have tried to make Adam and Eve something they were not: obedient. For some reason, they think that making our First Parents into something they weren't will give them greater honor or respect. This simply isn't true. Adam and Eve were without doubt amazing people, but they acted against a commandment of God, and that's a sin, for "sin is a transgression of the law." (1 John 3:4). For details, please click the link. Curiously, this entire issue has nothing to do with your question, but it was brought up as important by Paul Draper and so needed to be addressed.

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The relevant verse from the Book of Mormon is this one:

And they would have had no children; wherefore they would have remained in a state of innocence, having no joy, for they knew no misery; doing no good, for they knew no sin. (2 Nephi 2:23, emphasis mine)

That's would, not could. Dogmatically there was no physiological condition preventing Adam and Eve from conceiving children in the Garden. So why wouldn't they? This verse explains that Adam and Eve were innocent. OK, what does that mean?

Every spirit of man was innocent in the beginning; and God having redeemed man from the fall, men became again, in their infant state, innocent before God. (D&C 93:38)¹

Considering that the LDS Church believes there was a council in heaven before the world was created during which Lucifer and a third of the host of heaven rebelled against the Father and were cast out, it's a head-scratcher as to why the Lord would tell Josph Smith that before birth into mortality, every spirit is innocent. The answer is a few verses earlier.

For man is spirit. The elements are eternal, and spirit and element, inseparably connected, receive a fulness of joy; and when separated, man cannot receive a fulness of joy. (D&C 93:33-34)

Humanity is innocent of what it means to be mortal before birth into mortality, which includes the ability to procreate. And since disobedience had never before occured and the knowledge that there might be something other than saying "hi" that humans might do had not yet been introduced to the earth, they were stuck, innocent, doing a whole lot of nothing. Which is what we read from the preceeding verse in 2 Nephi.

And now, behold, if Adam had not transgressed he would not have fallen, but he would have remained in the garden of Eden. And all things which were created must have remained in the same state in which they were after they were created; and they must have remained forever, and had no end. (2 Nephi 2:22, emphasis mine)

These statements make some assumptions.

1. That Adam and Eve would never have been enticed of their own selves to sexual activity.

2. That Adam and Eve were not strong enough to avoid all temptation.

Earlier still in the same scriptural discourse we read:

Wherefore, the Lord God gave unto man that he should act for himself. Wherefore, man could not act for himself save it should be that he was enticed by the one or the other. (2 Nephi 2:16)

Here's where we finally start understanding the problem. Our Heavenly Father wants us to be free, but the only way to be free is to have the power to choose between good and evil, and that was something Adam and Eve did not yet know how to do. They didn't even know the difference between good and evil.

So, how does a mortal parent teach a 6-mo-old child that embezzlement is wrong? That's a mighty complex sin for a very innocent child. What they do, of course, is educate the child — a process that takes years.

Our Heavenly Father used the same process, He just didn't need that much time.

And I, Lehi, according to the things which I have read, must needs suppose that an angel of God, according to that which is written, had fallen from heaven; wherefore, he became a devil, having sought that which was evil before God. And because he had fallen from heaven, and had become miserable forever, he sought also the misery of all mankind. Wherefore, he said unto Eve, yea, even that old serpent, who is the devil, who is the father of all lies, wherefore he said: Partake of the forbidden fruit, and ye shall not die, but ye shall be as God, knowing good and evil. (2 Nephi 2:17-18)

To this we need to add one key concept that LDS members learn from the Temple endowent: the decision to let Lucifer tempt Adam and Eve was the Father's.

This is unbelievably important.

• The choice to eat the fruit was Adam's.
• The choice to let Adam be tempted was God's.

We believe that men will be punished for their own sins, and not for Adam’s transgression. (Article of Faith #2)

50% of the reason for Jesus' atoning sacrifice is that being tempted wasn't Adam's fault. But the consequence of Adam's choice affected everybody. A balance had to be restored, and Jesus restored the balance.

The result is that everyone now has access to knowledge and are afflicted by temptation, granting us the privilege of choice, which includes the privilege of choosing to bring children into this world.

Regrettably, there is a component of "we don't know" that must be addressed

The astute observer will notice that I didn't address assumption #1, that Adam and Eve would never be enticed of themselves to sexual activity. And if we pay attention to what Jacob said, "would" vs. "could" doesn't actually matter because he's discussing a consequence of being in the state of perpetual innocence that they "must" have been in (2 Nephi 2:22-23). Grammatically, they couldn't have had children. But this not because of a physiological difference that we don't now a blooming thing about and can only assume or speculate, it's because of the innocence of spirits when first brought into a mortal body and are then left without influence (the influence of knowledge or temptation).

They didn't know how to procreate and there was no enticement to learn.

In other words, we simply do not know if Adam and Eve could have physiologically conceived children before the Fall and if they could, we do not know if (given the possibility of an infinite amount of time) whether or not they would have eventually discovered their sexuality.

About this aspect we do not know. From the perspective of fallen Man we simply don't have the perspective to answer that question. Our only point of reference is a laughing happy baby... which does not have any sexual proclivity.

We also don't worry about it as it isn't how events played out.

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_{¹ This is one of the two scriptural reasons why the LDS Church does not endorse infant baptism (the other being Moroni 8:5-8). Due to the atonment of Christ, all people born into the world are as innocent as Adam and Eve were before the Fall. And just as Adam and Eve had to learn (via the Tree of Knowledge of Good and Evil), all children must learn, and will not be held accountable until they have.}