If you're going to try to unravel mysteries, your speculations might as well be logical and plausable ones.
Let's look again at those Lincoln County census entries for Isaiah Abernathy, and indulge in some "what if's..."
If Isaiah was born in the late fall of 1790 rather than in 1792, then the tally marks for him on all of those early ones are still consistent, and the one that looks like it might be off is the 1840 one. Depending on what month in 1790 he was born, he might not yet be in the 1780-1790 bracket where one would expect to find him in that census enumeration, in which case it wasn't off at all. The earlier census records were also consistent in showing Sarah in the same age bracket as Isaiah. If she were 18 or 19 years old when she married Isaiah in 1813, then she was born abt 1794 and would have been very near the end of her childbearing years by 1835. Not so near that she couldn't have one or two more, but near enough that it might have been less than desirable, if not too much. It is therefore possible that she died from complications after the birth of that last infant.
The son and daughter born between 1835 and 1840 don't appear to have been found again. They are certainly not the twins Lawrence and Teletha found with Matthew and Eve in 1860 in the household of Caleb (40) and Isabella (38) Eaker. If the ages on that census are correct, it is just barely possible that Eva was Matthew's mother rather than his elder sister. Eva may also have been the mother of Lawrence and Teletha. It is thus, not impossible, that Lawson _was_ Matthew's father but that his mother was Eve and not Lawson's legal wife, Margaret Rankin. In fact, that may have been one contributing factor in Lawson's return to NC by 1850.
Now, granted, all this is speculation, but the technology of today does hold out some hope of unraveling brick walls. Even ones as solid as this one appears.
As you may know, I am involved in a DNA project that attempts to classify Abernethy/Abernathy lines according to both paper trails and Y-DNA results. Last year I traced a volunteer's lineage back to Nathan Abernathy and Eve Cline. I assumed that all the traditional research assigning that Nathan to Miles and Ursula and thence to the Robert Abernathy Lineage were valid.
So I was rather startled (to say the least) to find that our volunteer's lineage was so VASTLY different that that there was no way he could have descended from Robert. Either we had a "non-paternity event" or my research was badly off or the traditional research was what was off in left field somewhere. I have been attempting to find direct male descendants of Nathan and Eve in order to determine which of those three alternatives holds true in this instance, as well as to provide enough data to begin to define a solid "profile" for Nathan's line. It is advisable to have a minimum of data from three or more to exclude the possibility of non-paternity events and fully establish a line's profile.
However. From your point of view the following conditions obtain.
IF a direct male descendant of Lawson can be persuaded to have his DNA tested and
IF a direct male descendant of Matthew can also be persuaded likewise and
IF the results match each other closely enough
then they could, indeed, descend from a single common ancestor in a previous generation.
IF they also come close to matching any of the Y-DNA data we have to date on some 15 volunteers, then your brick wall might just come crumbling down in a hurry.
It might be a sticky wicket, because while finding an illigitimate ROYAL in one's ancestry is somehow quite desirable, finding one who's less than royal is somehow very much less so. And when someone has grown up all their life believing one thing they can initially get rather hostile when scientific evidence challenges or disproves it. But while paper trails can become cross-linked by inexpert researchers and the error strongly entrenched by subsequent researchers who don't verify the data well enough or sumply copy the information on blind trust, Y-DNA values, however difficult they might be (initially at least) for some of us to unravel, don't lie.