The story of the slave who pulled a thorn from a lion's paw is called "Androclus and the Lion." The story did not originate in the Bible, but in the fifth book of "Attic Nights" by the Roman author Gellius.
The original version of "Androclus and the Lion" is told as an eyewitness account from a spectator at the Roman Circus Maximus. A slave, Androclus, is brought out to be eaten by a lion, but when the lion sees him, it fawns over him like a dog. Androclus relates his story of how he escaped his master and hid in a cave where he found a lion with a splinter in its paw to Gaius Caeser. Androclus removed the splinter, and the lion repaid him by giving him food and shelter for the next three years. Androclus then left to return to civilization, but he was captured and condemned to death in Rome. By serendipity, he was put in the arena with the same lion he healed, which had also been captured. This story prompts the public to demand Androclus' freedom, and he becomes a free man with the lion as his companion.
Aesop later used this story in his book of fables, appending to it the moral lesson "gratitude is the sign of noble souls." The Catholic faith attributes the story to the life of St. Jerome, stating that he treated a lion's paw and in return the lion watched over his monastery. The story is also used as an allegory in "Gesta Romanorum," where the lion is the human race and the thorn original sin, pulled from its body by baptism.