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"My dad wasn't just my dad, he was my best friend," she wrote in the Instagram caption. "He wore his heart. He didn't hide it; he wasn't afraid of love."
"My dad simply wanted to share laughter and love with this world," she added.
Shawn Ehlers/Getty for Scleroderma Research Foundation
In the touching tribute, Lara confessed, "I have noticed how scary it can be to love that big, to open so fully. It can be easier to be angry, fearful, negative."
"Maybe because love has an infinite quality, it is boundless," she continued.
"My dad taught me that it doesn't matter what life throws, how hard, how painful, how seemingly impossible. It doesn't stop that love," she said. "He chose love, always."
Sharing that she is committing "to doing the same," Lara explained, "The love is right here."
"And it's my responsibility to give it to myself and to share by living in the love," she concluded. "I love you infinitely, dad. Happy Father's Day."
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Saget died on Jan. 9 at age 65. He was found in his hotel room at the Ritz-Carlton in Orlando, Florida, one day after performing a stand-up special outside Jacksonville. An autopsy later revealed he had died from head trauma consistent with some kind of fall.
In addition to Lara, Saget shares daughters Aubrey, 35, and Jennifer, 29, with ex-wife Sherri Kramer.
Last Sunday, the beloved comedian was posthumously given the Impact Award at the Fourth Annual Critics Choice Real TV Awards in Los Angeles.
His longtime friend and Full House costar John Stamos was on hand at the Fairmont Century Plaza to present the honor, a career achievement trophy given for performers with a long legacy of accomplishment in nonfiction, unscripted and reality television.
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Saget's widow, Kelly Rizzo, accepted the award on behalf of her late husband.
On the red carpet, Rizzo spoke to PEOPLE about how proud the honor would have made him, praising his work as host of America's Funniest Home Videos.
"He was one of the pioneers in the reality TV world," she explained of the long-running series, which Saget hosted from its debut in 1989 through 1997.
"It's just so special to be here to honor him, but also still so weird and surreal at the fact that he's not here," she added.
"This is the first red carpet I've done without him. It's very strange. I feel like he's waiting in the wings and he'll be like, 'Honey, I'll be there in a few minutes.' It still doesn't feel right, but all we can do is our best and be here to celebrate him and his legacy. That's all I want to do."