John Leiche Esq. of Carden, Sergeant. at Law

On the site of princely Chatsworth stood the homestead of Chetal, the Saxon, who was lord of the manor before the Norman Conquest; the ancient name of Chetesvorde (or, as Lysons says it should be, Chetelsvorde) bearing evidence of such a fact. Could we have known Lysons we would have submitted that this was simply the omission of the letter “1” by that dexterous scribe whose penmanship still excites curiosity after eight hundred years. Some three centuries subsequent to the Norman subjugation, there arose the half stone and timber residence of the Leches, which Sir William Cavendish purchased from the Agards about 1556-7, and evidently pulled down to build the edifice of which there is a painting extant.

http://cheshire-heraldry.org.uk/visitations1613/1613.pdf

On the west wall of the south transept, Chester Cathedral, is an oak tablet, by Randle Holme,

"to the memory of "John Leche of the Citty of Chester Alderman dyed on the 27 th day of Decemb: 1639."

In the rear of the banqueting hall, on the ground floor, is a small room panelled all round with oak. The window opens upon what was formerly called the Court-yard. Although it is now only fifteen feet by twelve feet, it was originally much larger and continued under the gallery to the outside wall on the west side, and probably much further south.

The gallery on the west side is five feet six inches in width, and rests on a massive carved beam supported by a fine fluted oak column with stone base. In the upper portion are thirteen flat oak pilasters, of Jacobean design, filled in with plaster.

This, with the plaster decorations of the lion rampant of Scotland, and the unicorn of Scotland, is further evidence that the building was erected subsequent to 1603. 

The gallery is known as “The Lady’s Bower,” probably owing to the fact that it was so named by the late Mr. T. P. Ivison, a well-known local artist, who executed a series of pen and ink drawings in connection with this house. It is entered from the landing by two steps. Below the treads is a moulding in which beautiful dentels are carved; and on the inner side of the doorway.

So Simpson's case, built on the church records and decorative style is that the house, or at least the decoration of the house, dates from the time of James I (1603-1625). Later writers seem to agree with him, dating the two "closets" around the rear courtyard and the "Lady Bower" to the early 17thC.