"My father just let my family and [me] know, amongst other [things] that he had another child after my little sister Aliana," Lohan, 22, writes in a post titled "Random Thoughts."
She continues: "Or maybe he had it before Aliana?? Either way, he cheated on my mother and that really sucks."
In an e-mail to PEOPLE, Lindsay's father, Michael Lohan, strongly denies his daughter's claim, and said in a separate conversation he believes there is a "99 percent chance" Lohan's MySpace message was actually written by her girlfriend, Samantha Ronson.
Noting on MySpace that she's "going through a lot right now," Lindsay grows introspective in her post.
"I think that people go through a lot in life," she writes. "And the things that we go through, whatever they may be, simply just make us stronger in the long run. That is, if we actually take what it is we have learned from our mistakes and teach ourselves what NOT to do in the future."
Likens Self to BritneyIn her post, the actress also says she plans to spend the holidays in Los Angeles with girlfriend Samantha Ronson.
"It is the first one I am spending away from home," Lohan writes. The actress also sends out holiday wishes to her mother, grandmother and siblings, Aliana, Cody and Michael.
Lohan also says that she identifies with another celebrity who has struggled publicly this year: Britney Spears.
But Lohan looks to Spears's recent comeback – her successful new album Circus and upcoming tour – as another learning opportunity.
"[Upheavals teach] young girls and boys that there are certain things in life that you should not let get in the way of your dreams and accomplishments," she writes. "At the end of the day, you have to look at yourself in the mirror and see who you really are."
Continues the post: "So YAY Britney for just being you and still following through with your dreams."
Reporting by DIANE HERBST and LIZ MCNEIL