Altman died on Monday night in Los Angeles at the age of 81.
Lohan says, "I feel as if I've just had the wind knocked out of me and my heart aches."
In a statement issued by her publicist, Gary Mantoosh, the 20-year-old sends her condolences to Altman's family and friends and says the director "made dreams possible for many independent aspiring filmmakers."
The Mean Girls star, who has had a troubled relationship with her imprisoned father, Michael, also calls Altman, "the closest thing to my father and grandfather that I really do believe I've had in several years."
She finishes the letter by saying, "If I can do anything for those who are in a very hard time right now, as I'm one of them with hearing this news, please take advantage of the fact that I'm just a phone call away."
Lohan then signed the letter, "God Bless, peace and love always. Thank You, Be Adequite (sic)."
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