Hi Anna, I've only had a look at the Lancashire Online Parish Clerks website, and not tried to find if the original records are anywhere but there are some issues.
The burial of the wife (not named in the record) of John Townley, esquire takes place on 28 Aug 1606 at St Peter, Burnley, Lancashire, and for John Townley, Esquire on 4 March 1607/08 (at WikiTree we use Gregorian or New Style dates, so it should be entered as 4 Mar 1608).
So if Sir John Townley was knighted then the burial information must be for a different couple? If he wasn't knighted then this could be them, but we would need to remove the Sir from his profile and Mary Townley, wouldn't be Lady Mary.
There is also an issue with the profile of the son Richard, as he is said to be born in 1566, but married on 10 Feb 1579/1580 which could indicate there is a chronological problem, though the year of birth isn't sourced, and I couldn't find it in the baptism records from the Lancashire Online Parish Clerks database.