The name is likely to be from Lesnes Abbey at Abbey Wood in Kent (now S.E. London). This was founded as an Augustinian house by Richard de Luci in 1178, it is said as penance for his part in the murder of Thomas Becket. The Abbey held a large amount of land amongst which it is supposed was the manor of Thorney Lezons.

Lesnes was the name of the half-hundred in which the Abbey stood. There seems no evidence tof a link to  a place in France.

Copinger in his Manors of Suffolk says the manor of Thorney Hall was granted by Henry II to Richard de Luci who we suppose granted the portion that became Thorney Lesnes to the Abbey,

  He also says that in 1543 after the dissolution Lezons was held by Robert Downes, he died in 1547 and passed it to his son Frances,  in 1555 it was sold to John Keble son of Robert Keble in 1606 it was sold to Robert Broke who died 1626,  it then remained in the Broke family of Brokes Hall, Nacton until at least 1714. In 1749 it was vested in William, Earl of Jersey.In 1835 it was vested in Edward Beck.
From 1800’s see also Thorney Mumpliers and Thorney Braziers, when all were held by held by Edward Beck esq (Neil Langridge, 2021)