“My wife says I’m the most obnoxious grandfather in the world," Biden said. "No. Wrong. Frank was the most obnoxious.”
Biden, who is known for his affinity for Amtrak, also joked that Lautenberg got more love from the train company, which named a train station for him and -- Biden joked -- held trains when Lautenberg was running late.
"I saved Amtrak three times before he was elected. I don’t know how the hell this happened," Biden said. "That’s mostly true.”
Biden also noted that he, as a longtime former senator, has often been asked to deliver his colleagues' eulogies -- even that of Republican former senator and one-time segregationist Strom Thurmond (R-S.C.).
"I knew Strom Thurmond so well, literally, I was asked to do his eulogy. I did his eulogy," Biden said, before delivering the punchline: "This is a lot easier."
(For the best of Biden from Wednesday, check out our recap on The Fix.)
Biden talked plenty about the senator, too, hailing him as a man of conviction who fought for his beliefs and worked extremely hard.
“He never ever backed off his political convictions for expediency," Biden said, concluding: “As the Irish would say: He was a man. He was a real man.”
Hillary Rodham Clinton also remembered Lautenberg as a fearless fighter for his beliefs and a progressive champion.
"As Frank would say, it’s not where you sit, it’s where you stand. And there was never any doubt where he stood," the former secretary of state and first lady said.
Clinton added that Lautenberg was the epitome of what a senator should be, noting his role in passing a smoking ban on airlines and his close relationship with the women of the Senate. She said he was considered an honorary member of their caucus.
“He dared greatly, and he led boldly, and we are safer, stronger and more prosperous because he did," she said.
Sen. Bob Menendez (D-N.J.), the first colleague to speak at Lautenberg's funeral, held the five-term senator up as a model of the American dream and hard work.
"Anybody who knew Frank knew that he was destined to make something of himself. And he did," Menendez said, adding: "I will remember his life as a testament to what is possible to achieve in America."
Later, in a light-hearted moment, Menendez addressed Lautenberg's widow, Bonnie Englebardt Lautenberg.
"Bonnie, I’m sure you know he loved you dearly," Menendez said. "Even Lady Gaga couldn’t lift a finger to you."
Lautenberg, who died at 89 on Monday, developed an affinity in his later years for the music of New Jersey native Lady Gaga, and he even held political fundraisers at her concerts.
Lautenberg's children also looked back at their father with humor.
His daughter, Lisa Lautenberg Birer, approached the podium with a hoarse voice and joked that her father had quieted her because she asked too many questions in her younger days -- something he took as challenging his authority.
One of Lautenberg’s two stepchildren, Lara Englebardt Metz, later noted that she had been asked to do a school report on the ban on smoking on airplanes.
She said she showed up to school with a taped interview with the bill’s sponsor, her stepfather, and received an A for her report.
His son, Josh Lautenberg, said that as recently as 10 days ago, the senator said he regretted his decision not to seek reelection in 2014.
Lautenberg famously regretted his decision to retire from the Senate in 2000, and in 2002 he returned to the chamber after becoming a late ballot replacement for embattled Sen. Robert Torricelli (D-N.J.).
Updated at 2:18 p.m.