The singer, who described the tragic celebrity as her "friend", shared a snapshot of some news articles on Instagram alongside a lengthy message.
Passing on her love and support to his family, Lindsay admitted her heart was "broken" following the news, before slamming Hollywood.
She wrote: "This is the result of #hollywood a beautiful life has come to an end.. A brilliant actor and a loving friend. Surround your life with good people and know who your #true #friends are my prayers and love goes out to anton's family #anton.
This breaks my heart. He was my friend I am so sorry to Anton's father."
The Star Trek actor, who was just 27 years old, was found dead in the driveway of his home in the early hours of Sunday morning after he failed to show up at an 11pm Saturday night rehearsal.
His worried friends visited his San Fernando Valley home around 1am to check on him and found him pinned between his car and the security gate at the bottom of the driveway which is on a steep incline.
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According to TMZ , he had just left home and had cleared the gate but then, for an unknown reason, got out of his car which he left in neutral.
He was pronounced dead at the scene, though a coroner is still to determine whether he died instantly on impact.
A statement from his spokeswoman released on Sunday said: "Actor Anton Yelchin was killed in a fatal traffic collision early this morning. His family requests you respect their privacy at this time."
Tributes have come pouring in for the actor since news of his tragic death broke.
His Star Trek co-star John Cho wrote: "I loved Anton Yelchin so much. He was a true artist - curious, beautiful, courageous. He was a great pal and a great son. I'm in ruins."
And filmmaker Kevin Smith described the news as "so damn sad".
While Zachary Quinto, who plays Spock, posted a picture of the actor and praised his enormous talent.
“Our dear friend. our comrade. our anton. one of the most open and intellectually curious people i have ever had the pleasure to know. so enormously talented and generous of heart.
"Wise beyond his years. and gone before his time. all love and strength to his family at this impossible time of grief."
Star Trek director JJ Abrams also penned a heartfelt tribute.
"You were brilliant. You were kind. You were funny as hell, and supremely talented. And you weren't here nearly long enough. Missing you... JJ."
