Conflicting theories?

       According to one online source; which mentions both options.  
"The lake was probably created during the construction of the canal in 1771. At that time, the hall was owned by Thomas Clifford, the fourth son of Hugh Clifford, 3rd Baron Clifford of Chudleigh, and the grounds had been designed on the advice of the landscaped architect Lancelot "Capability" Brown.  It is said Clifford "gave permission for the canal to pass through his land on the condition that it was made ... wide enough to look like a lake from the house" and thus in order not to spoil the view.
       More on lake later.
"Edward Aston (1494-1568) a prominent Staffordshire protestant, built an Elizabethan Hall at Tixall in 1555".  -  from A. N. Other -   "The hall was eventually taken down in 1928/9, with some of the stone being used to build St John's Church chancel at Littleworth, Stafford." Leaving only the "Gatehouse" - above.
The Gatehouse was "Built circa 1575 and a very stylish specimen of Elizabethan design. Ashlar faced and retangular with octagonal ogee-domed turrets at the angles and central. archway. 3 storeys, each decorated with an Order of columns: Doric, Ionic and Corinthian, Balustraded parapet."

       "More on lake."  -  The same page as seen above, also said:-
"It has also been suggested that the canal was routed to utilise a lake that already existed, in which the angler and writer Izaak Walton had learned to fish."
SO
To lapse into my native tongue - It would appear that - "Nee body Knows." with 100% certainty.