Short answers, pulled from the story.
Sir Thomas Lucy (the 24th of April 1532 - the 7th of July 1600) was an English politician and magistrate in Warwickshire who sat in the House of Commons in 1571 and 1585. He is best known for his alleged conflicts with the young William Shakespeare, including stories of poaching, a mocking ballad, and possible satirisation as the character Justice Shallow.
The poaching story was first recorded by Richard Davies in the late 17th century and repeated by Shakespeare's first biographer Nicholas Rowe. No surviving legal records confirm or disprove it. Critics note there were no deer at Charlecote until after Shakespeare's death, though Samuel Schoenbaum pointed out that Lucy held a free warren that could have supported rabbits, hares, and other animals.
The theory that Justice Shallow is a satire of Thomas Lucy dates to roughly 1688-1700. The Merry Wives of Windsor contains a pun on luces (pike fish) in a coat of arms collapsing into lice, matching Lucy's actual heraldry. Samuel Schoenbaum considered a direct parody unlikely, and Leslie Hotson argued the real target was William Gardiner, a corrupt Justice of the Peace whose arms also contained luces.
Lucy was an ardent Protestant activist and loyal supporter of Queen Elizabeth. He arrested and interrogated Catholic families following the missionary activities of the Jesuit Edmund Campion. After the Somerville plot of 1582, he raided homes of the Arden family, to whom Shakespeare was related, and took part in the arrest of Edward Arden in 1583.
Thomas Lucy lived at Charlecote Park near Stratford-on-Avon, Warwickshire. The house was rebuilt in red brick around 1558 by a builder known as John of Padua, also recorded as John Thorpe. Queen Elizabeth visited Charlecote Park in 1572.
Thomas Lucy died on the 7th of July 1600, in the midst of a local scandal involving a granddaughter who had eloped with a family servant. His son inherited the estate, and his grandson Thomas also served as MP for Warwickshire.