Ms Asplund, at just five years old, lost her father and three brothers - including a fraternal twin - when the "practically unsinkable" ship went down in the North Atlantic after hitting an iceberg.
She died at the weekend at her home in Shrewsbury, said Ronald E Johnson, vice president of the Nordgren Memorial Chapel in Worcester, Massachusetts. "She went to sleep peacefully," he said.
Ms Asplund's mother, Selma, and another brother, Felix, who was 3, also survived the Titanic sinking in the early morning of April 15, 1912.
Ms Asplund was the last Titanic survivor with actual memories of the sinking, but she shunned publicity and rarely spoke about the events.
At least two other survivors are living, but they were too young to have memories of the disaster. Barbara Joyce West Dainton of Truro, England, was 10 months old and Elizabeth Gladys "Millvina" Dean of Southampton, England, was 2 months old.
The Asplund family had boarded the ship in Southampton, England, as third-class passengers on their way back to Worcester from their ancestral homeland, Sweden, where they had spent several years.
Ms Asplund's mother described the sinking in an interview with the Worcester Telegram & Gazette newspaper shortly after she and her two children arrived in the city.
Icebergs in the distance
Selma Asplund said the family went to the Titanic's upper deck after the ship struck the iceberg: "I could see the icebergs for a great distance around ... It was cold and the little ones were cuddling close to one another and trying to keep from under the feet of the many excited people ... My little girl, Lillie, accompanied me, and my husband said 'Go ahead, we will get into one of the other boats.' He smiled as he said it."
Because they lost all of their possessions and money, the city of Worcester held a fundraiser and a benefit concert that together brought in about $US2,000 for the surviving Asplunds.
Lillian Asplund never married and worked at secretarial jobs in the Worcester area most of her life. She retired early to care for her mother, who was described as having never gotten over the tragedy.
Selma Asplund died on the 52nd anniversary of the sinking in 1964 at age 91. Felix Asplund died on March 1, 1983, at age 73.
A memorial service will be held on Wednesday, Mr Johnson said.
A British-based auction house announced at the weekend there was no winning bid in an auction for a worn beech wood recliner reportedly snatched as a souvenir from the Titanic.
The bidding topped out at $US62,000 ($A80,000), short of a confidential sale threshold set by its anonymous seller, said Josephine Olley, a spokeswoman for Bonhams & Butterfields.
Bonhams & Butterfields will now try to sell the chair privately. The deck chair, with a fold-out footrest, was one of more than 2,500 lots on the block this weekend at a collectables auction.
Bonhams & Butterfields says the deck chair is one of only six left in world.
The ocean liner struck an iceberg on its maiden voyage and went down in the North Atlantic in April 1912, killing about 1,500 people.