Elroy "Lucky" Kleinschmidt got his nickname from an incident at a Costco store where he went in to buy a new winch, realized he had to go to the bathroom, and slipped in a puddle of pee-pee (urine). The resulting injury left Lucky in constant pain. Lucky sued the store and received a $53,000 cash settlement, which caused his friends to see him as lucky -- hence, the nickname.
Lucky refers to the cash settlement as "mah pee-pee money," and one of his catchphrases is "I done slipped on pee-pee at the Costco." The Costco story is partially contradicted in the episode "Luanne Gets Lucky," where Lucky says that he was at the store purchasing a TV, rather than buying a new cable for his winch, and again during the series where he states "If I hadn't gone to get a cash advance, I wouldn't have slipped on pee-pee, wouldn't have got my settlement money, and never would have bought these rims ... it's scary to think about the road not traveled".
Lucky claims he will never have to work another day in his life, even though the Costco settlement isn't nearly enough to provide for his needs for the rest of his life. After the Costco "pee-pee" incident, Lucky made a vocation of going into stores, intentionally injuring himself, and suing the owner. Lucky actually manages to make a decent living this way.
Although at one point (episode (213) "Lucky's Wedding Suit" Season 11 Episode12), his funds had dwindled to $9,000, and Hank referred Lucky to Dale's Dead-Bug for some temporary work. Lucky and Dale did some horsing around on Dale's basement steps, the railing collapsed, and Lucky fell, injuring his back. With some regret, Lucky filed a lawsuit against Dale. However, events quickly spun out of control, and Lucky's attorney threatened to sue Strickland Propane instead (on the grounds that Hank was acting as a Strickland employee when he referred Lucky to Dale), correctly sensing higher fee potential in suing Strickland than in suing Dale. With the help of Dale and Hank, Lucky was able to manipulate things so that the attorney would come out on the wrong end of a lawsuit, and the attorney ended up cutting Lucky a check for $53,000 (His "usual lawsuit fee and not a penny more") to make the whole thing go away.
Lucky has a definite tendency toward scam artistry, as seen in his lawsuit against Dale and subsequently getting a settlement from his own attorney. Lucky also went to great lengths to avoid paying a garbage-pickup tax, claiming the tax to be "un-American", by placing his garbage into Hank's garbage cans. Lucky is also somewhat dim: He once cut his hand on barbed wire and refused to go to the hospital because (he says) his family has a long history of getting shot in the woods and dying in hospitals.
In spite of his flaws, Lucky is a genuinely good-hearted person: He cares deeply for Luanne and always tries his best to do right by her. In "Edu-macating Lucky," where they learn that Luanne is pregnant, he tries to get his GED so that he'll be worthy by his own code of honor to ask Luanne to marry him. Lucky fails, due to Peggy intentionally tutoring him with wrong information (to which she later confessed), so he asks for and receives a shotgun wedding from Hank, thus doing the right thing by Luanne while remaining true to himself -- and finally being welcomed into the Hill family. Lucky also shows his devotion to Luanne in the episode "Life: A Loser's Manual" when he protects Luanne from learning that her father is in prison, preserving Luanne's good image of her father by allowing her to continue believing that he is an oil rig worker instead of a convict. He also cares for her non Imediate family by showing he would go to great lengths to get Bobby a corn chip "fresh off the line" which also presented another example of his inclination towards workplace lawsuits.
Additionally, Lucky is deceptively perceptive, mainly due to his extensive watchings of daytime detective shows, and his own personal experiences. He figures out that Luanne's father isnt actually working on an oil rig when he mentions that cigarettes are like currency on the oil rig. He also knew all along who made the footprints on the mirror in the train bathroom during Peggy's birthday when it seemed as if it were going to remain an unsolved mystery.
Lucky's and Luanne's daughter Gracie is born in the episode "Lucky See, Monkey Do." Lucky believes that "She carries a strong resemblence to my side of the family.. though that may change once she gets teeth."