There are numerous family trees relating to the various English royals of different time periods, and Katherine and John are no exception. Since John of Gaunt's family name was Plantagenet (the dynasty of his family, like the Windsors, Tudors, Stuarts, etc.), his family history is very easy to find.
Start with a search engine and enter their names. In the time it took you to write your question here, you could've gotten thousands of search results ranging from official British peerage websites to mom-and-pop pages with someone's personal genealogy.
Katherine's maiden name is actually ROET. She married a Swynford prior to her relationship with John of Gaunt. Her parents were Payne De Roet and Catherine of Hainault.
Katherine was born November 25, 1350 and died May 10, 1403. She and John of Gaunt had four children, and John's parents were Edward Plantagenet (Edward III, King of England) and Philippa Van Holland of Hainault.