The Mean Girls star's father and his wife Kate Major welcomed son Logan Michael Lohan on New Year's Eve. He weighed in at 6lbs 14oz.
In a statement to US Weekly, the new parents said they were "ecstatic" about what they called a late Christmas gift.
"What a way to bring in the New Year!" said Michael.
Michael and Dina are already parents to son Landon, who turns two this month. Michael is also father to four children, including Lindsay, with ex-wife Dina Lohan.
Lindsay, who spent the New Year with her mother Dina and younger sister Aliana, has not commented on the new arrival.
Instead, she simply tweeted this week: "xoxoxox grateful for my family, friends and a new year to come with lots of work!"
Lindsay and her father are known to have a tempestuous relationship.
Actress Lindsay spent the New Year with her family in the US after returning from a Christmas break to French Polynesia with pals.
Unfortunately for Lindsay, she contracted the mosquito-borne virus Chikungunya while on her travels, but told fans she was refusing to let it spoil her otherwise idyllic holiday.
Celebrities who welcomed babies in 2014:
Copyright: Rex Features WENN/Matthew Taylor/Daniel Deme/Josiah True/Matthre Taylor/Joe