Once was near the trade deadline in 2016, the year they'd go on together to win their only championship. The other was last summer, when they thought they'd secured a deal for Paul George that Indiana pulled out of at the last second. His name popped up in trade rumors even beyond that.
Love was picked on by LeBron James, publicly (anyone remember the FIT IN tweet?) and privately, especially during his first two years here.
He was the one who had to change how he played to make it work in Cleveland -- not James and not Kyrie Irving — and coach Tyronn Lue got in Love's face more than once, to tell him to quit whining and demand the ball.
Love was the one taking criticism from all sides in the team meeting in January that tore the Cavs apart. He's been hurt in all of his four seasons in Cleveland, costing him appearances in two All-Star games.
And on Tuesday, in front of a bunch of construction workers in hardhats who are refurbishing The Q, Love — not James or Irving or any other Cavs star from the last four glorious seasons — was signing his name to a four-year, $120 million extension that could keep in Cleveland until he's 35.
The Cavs, now, are Love's team. He understands the reality and recognizes the irony that he's the one still standing in Cleveland among the Big 3.
"I look back, everything happens for a reason," Love said Tuesday afternoon at the Cavs' training facility in Independence. "My best friend from back home said, 'It always works out.' This is where I wanted to be. I've said that all along. There were some tough times where potentially I would have been traded and my name came up in rumors every few months. But hopefully that ends now."
Love, who turns 30 in September and has played 10 seasons, will be paid $24.1 million this year, on his original deal with the Cavs. The extension starts in 2019-20. Love eschewed the maximum raises available to him later in the deal. There is no player option or no-trade clause in this contract. The Cavs can't trade him for six months.
On Tuesday, both Love and Cleveland general manager Koby Altman said they expressed a mutual desire for Love to stay here long term immediately after the 2017 Finals ended. Altman said Love was his first phone call after learning that James was leaving for the Lakers — a call Love took after he had just heard the news while vacationing in the Hamptons.
"I looked him in the eye after the season and — he can attest to this too — I told him I want to be here and I want to be a part of this moving forward," Love said.
"I said, 'Kev, I'm not trading ya. I want you to be here and I want you to be a part of this thing,'" Altman said, relaying his July 1 conversation with Love. "He was all in then, too. He's never wavered in his commitment, not once in the four years since we traded for him and not once this summer and, to me, that's really, really meaningful. He wants to be a part of this franchise and be the leader."
Love averaged 17.6 points and 9.3 boards last season, and over four years here is averaging 17.1 points and 10.0 boards. He's shooting .377 from 3-point range as a Cav and shot a career-best .415 last season. He's made two of his five All-Star teams here.
However, Love's story in Cleveland is far more complex with its share of darker moments.
The Cavs acquired Love in the summer of 2014 for a trade in which they sent No. 1 overall pick Andrew Wiggins to the Timberwolves. He was a piece coveted by James, who was coming back to Cleveland to try and win the city its first title since 1964.
Love, who averaged 19.2 points and 12.2 boards in his six seasons in Minnesota, found himself as a distant third wheel in the early going in Cleveland while James and Irving dominated the ball. He had a sore back and he sulked as the Cavs struggled to either include him or use him properly. James called him out for it.
Just as Love started to find his way in his first-ever playoff appearance in 2015, he was lost for the remainder of the year when Kelly Olynyk ripped his left shoulder out of place in Game 4 of the Cavs' first-round series against Boston.
Love watched as the Cavs reached the Finals but lost to the Warriors in six games. He and James carried the Cavs for the first part of the following season, but fell into a familiar trap when Irving returned from a devastating knee injury suffered in the 2015 Finals.
Love was a free agent that summer, but after a meeting with James in Los Angeles in which they cleared the air a little he signed a four-year, $128 million deal.
The Cavs fired coach David Blatt in January of 2016 and replaced with Lue, and Lue's first words to Love and to Irving were that they needed to put their personal brands and aspirations aside and defer to James to win. Then-general manager David Griffin nearly traded Love shortly after that, as the burden of continuing to sacrifice was weighing on him.
Just before the start of the 2016 playoffs, Lue tore into Love again, this time imploring him to play like the three-time All-Star he was at the time and demand the ball from James and Irving.
The Cavs cruised through the Eastern Conference to the Finals, and early in that series against the Warriors Love was miserable. He struggled mightily against Draymond Green and suffered a concussion, causing him to miss a game and come off the bench in another. But in Game 7, Love finished with nine points and a game-high 14 rebounds, defended Stephen Curry furiously in the final minute, and the Cavs won their first and only title.
Love missed about six weeks in 2016-17 because of arthroscopic knee surgery, and even more time last season because of a broken bone in his left hand. He also disclosed for the first time that he was dealing with panic attacks.
"There's been tough times, but they've also let me be myself," Love said of the Cavs. "Whether it's been All-Star performances, whether it's been making it to the Finals, being in the Finals in 2016, the low moments, me coming out about mental health and having my back with that, you know it's been a special ride and I'm looking forward to it continuing."
Love's extension is the clearest sign yet that, as the Cavs have said for weeks, there will be no immediate rebuild in Cleveland with James gone. That's the imagery the organization was going for when Love signed his extension in front of the workers who are refurbishing, but not tearing down, The Q. Love was signing their hardhats and taking selfies.
Love is high on rookie point guard Collin Sexton and second-year forward Cedi Osman, and believes in returning veterans like Tristan Thompson and JR Smith and Kyle Korver and George Hill.
Larry Nance Jr., who was with Love at The Q on Tuesday, could soon sign an extension with the Cavs. Rodney Hood is a restricted free agent and will likely return.
The Cavs are under no illusion that they can realistically reach a fifth straight Finals — heck, neither nor the Cavs nor Heat even made the playoffs the first year after losing James. But this team would like to make the playoffs. Love talked about the Cavs "overachieving."
"It's almost like, to me it's not a rebuild, because we have talent, we have championship caliber guys, and we have young and fresh guys that are going to be willing to learn and come along in this league as i mentioned. I think guys putting on their hard hats and coming to work every day," Love said. "That has to be the identity to our team, and I think we have guys that are cut from that cloth and are going to be willing to go out there and prove themselves.”