“He had, by a misfortune common enough to young fellows, fallen into ill company; and amongst them, some made a frequent practice of deer-stealing, engaged him with them more than once in robbing a park that belonged to Sir Thomas Lucy of Charlecote, near Stratford. For this he was prosecuted by that gentleman, as he thought, somewhat too severely; and in order to revenge that ill-usage he made a ballad upon him. And tho’ this, probably the first essay of his poetry, be lost, yet it is said to have been so very bitter, that it redoubled the prosecution against him to that degree, that he was obliged to leave his business and family in Warwickshire, for some time, and shelter himself in London.”

So Rowe maintains
Shakespeare poached deer from Charlecote
He was prosecuted for it by the local magistrate, Thomas Lucy
As a result Charlecote was responsible for Shakespeare’s first verse
Other sources maintain this was pinned to the gates of Charlecote (the earliest was by a man who died in 1703 which is as close as we can get to a contemporary account)
Charlecote was responsible for Shakespeare going to London.

There seems to be only anecdotal evidence for any of this. We cannot even be sure Shakespeare was hauled up in front of Thomas Lucy. But the story persists partly because the Lucy family accrued benefits from it.
However Shakespeare had moved to London by 1592 but Charlecote did not request official consent to establish a deer park until 1615 so there were no deer at Charlecote when Shakespeare lived in Stratford.