Thomas S. Lunt did a good job with his book. There are various other works that extend what we know about the descendants of Henry and Ann Lunt (example web site).
While looking at a site today, I saw that Sarah Osgood had married Joesph Lunt. On looking at T.S.'s book, I see that Joseph is #66. He is the son of Joseph Lunt (#15) and Martha Noyes. Martha was a descendant of Rev. William Noyes through his son, Rev. Nicholas Noyes.
Now, Sarah is interesting. She is the offspring of families that were troubled by the Witch Trials of 1692: Osgood, Dane, Clements. Her grandmother was Mary (Clements) Osgood who was accused. She is descendant of Rev. Francis Dane who was a vocal critic of the whole affair (Imagine a meeting).
T.S. mentions nothing further about Joseph and Sarah. But, on a closer look (Mass Vital Records), we see that they had a daughter, Sarah, born in 1741.
The next step is to see what became of this Sarah Lunt. Those families experienced a lot of tragedy. We seem to romanticize the experiences of the witch trials, but those who suffered did so in a dire mode (to wit, the Wilson family and a medical affliction on a whole generation).
While reading through Massachusetts Soldiers and Sailors in the War of the Revolution (a 17-volume compilation authorized in 1891 - see below for on-line access to all volumes), I was struck by several things. For one, how can we thank those who put together this wonderful resource? The page count is above 17,000 which represents the effort to identify the patriots in one area. For instance, New Hampshire's patriots are not included, though Maine is well-represented.
Too, the Lunt listing (Volume 10) starts on page 44 with Abner and ends with Timothy on page 52. There are over 40 Lunts in the listing. Then, one has to wonder which of these are descendants of Henry.
An open task will be to identify Lunt families who were early emigrants and to pull out of the MS&S those who were offspring of Henry and Ann. We can start with Thomas S. Lunt's book.
--- Index to on-line volumes (thanks to archive.org) --
Paula's Genealogy Corner has been a real asset during my studies of Henry's offspring and the collateral families. Paula's Lunt page goes through 4 generations for several lines. She takes Daniel (1st Gen) to Josiah who was born in 1732.
She also has the contents of Henry's (0th Gen) will. He mentions his wife as Anna.
This site is an example of several that we can organize into a reference page. Paula has been consistent in providing sources which can be found at the bottom of the page.