"Congratulations to my beautiful sister in law @ninaginz and my brother @mikelohan!!!" she wrote on her Instagram.
Lindsay, who has another younger brother Cody Lohan and a sister Ali Lohan, shared a picture of the happy couple on the social media but later deleted it.
The photo showed Michael, 28, and his fiancee beaming to the camera. The bride-to-be flashed her new diamond ring.
Lindsay herself is reported to get engaged to her Russian boyfriend Egor Tarabasov after several months of dating.
The 29-year-old star has not yet officially confirmed the rumor but she added fuel to it by wearing a huge emerald rock on her left hand.
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