Reportedly, the English Crown granted, on 7 Feb 1612, a lease of 29 acres of land in the village of Cowbit, near Spalding (Lincolnshire), to Francis Longland, gentleman, who named successors to the lease in the event of his death: Francis Billington, son of John Billington and Francis Newton, son of Robert Newton.
Reportedly, Mary Longland (widow?) named her son Francis Longland, her daughter "Katherine Newton" and her goddaughter (granddaughter?), Mary Newton, in her will of 20 August 1613 (where?).
As it appears that Francis Newton was a nephew of Francis Longland (the son of his sister Katherine), then here are some possibilities:
assuming that the wife of John Billington, Ellinor, was the mother of Francis Billington, then she could have been a cousin of Francis Longland, on her mother’s side or on her father’s side;
or, John Billington could have been a cousin of Francis Billington, on his father’s side or on his mother’s side.
If a cousin relationship was involved, it could have been from the family of Mary Longland or from the family of her apparently deceased husband, Mr. Longland; but, right now, we have only the Longland possibility to pursue as we do not know the maiden name of Mary Longland.
Certainly seeing a full transcript of the Mary Longland will of 20 Aug 1613 (along with any accompanying or related documents) would help, as we need to look at all the names involved and any references to land, etc.
It seems that if Mary Longland left a will then her husband would have left a will or estate record and discovering that or those would be of great help, as that or they could lead to land records and other records which might uncover the relationship of the Billington family to the Longland family.
If a cousin relationship between the Longlands and the Billingtons was involved then researching all the brothers and sisters of Mr. and Mary Longland might be necessary.
It would be worth the effort if it turned out that John Billington descendants were also descended from the Longland family (which is a distinct possibility).