Wills & Bequests

My guess would be that the boys had each received a larger piece of land, and/or that each of their children had received something at an earlier time.

It is also possible that Lucinda was recently a single parent through widowhood or divorce, or her spouse is a deadbeat dad--they did have them back then even if that was not the nomenclature of the day!

Another possibility is that Lucinda is disabled/sickly, and the cash award to her children is to be certain that they do receive something from her family, possibly because of the actions of her husband indicating he would sell the land & take off leaving the kids after her death.

I think Marie nailed most of it.  It is also possible that the named children of Lucinda were by a prior marriage and may not stand to inherit from Lucinda's husband at the time the will was written.

I would not assume that the named sons were married with children.  This point would need investigation.  From the given summary there is no reason to assume that the sons were close in age to Lucinda, although it is possible that the children were named in order of age.

While the will's text does suggest it is likely that each son was not a minor, I have seen a will specifying that a grandson live on and work the home farm with the testator's widow, who was to receive half the proceeds.  When this will was written in 1815, the grandson was not much more than 15 years old -- so there can be different views of when particular individuals were sufficiently grown to handle such things.  The grandson was by his mother's first marriage, and may already have been living with the testator since the boy's mother's remarriage more than a decade before.  In the case of the 1815 will there were also several nearby uncles who doubtless could be called on for help.

I have seen other wills specifying that a child be considered "of age" to receive considerable legacies at 14.  And there were children aged 10 and 12 who were active participants during the Revolutionary War.

Good question!

Another explanation might be that Lucinda was from a different marriage than the other children and had not received her mother's share. But in that case I would have expected to see her listed at the beginning or the end of the list. Perhaps Lucinda was the one who had promised to take care of dad until he died and in return he promised to provide for her children. Our maybe, Lucinda's children were his children too. We should never dismiss the illegal or immoral options beforehand. I've recently worked on a project that involved an incest case that went to court. Five children were born as a result of that relationship, including the client's grandmother. [The client has given me permission to refer to the case anonymously.]

It may be possible that the daughter, Lucinda, married in haste or against her father's wishes and did not receive her dowry upon marriage. Perhaps her father thought better of it at the end of his years and decided to give it to her children, instead. 
In addition, in that American era, women did not have land rights even though land might be willed to them. Their husbands would hold the right to the land. It is possible that the thousand dollars was in lieu of full title.

I have seen many wills in which granchildren, nieces or nephews are singled out for bequests because they are orphans (their fathers are deceased), and I would think that is the most likely explanation. 

In some cases special provisions are made if a son-in-law is in financial trouble.  Leaving a legacy directly to Lucinda would make it subject to her husband's debts, and so a bequest like this one might be a way around this type of problem.   There are probably better ways around this problem; however, if we can confirm that her husband was still alive, I would research his financial situation in tax records, lawsuits over debts etc. to determine if this is a possibility.