Michael, 52, - who has four children with ex-wife Dina Lohan including his 26-year-old actress daughter and is currently expecting a baby with his 29-year-old girlfriend Kate Major - has allegedly been avoiding taking the test for four years and according to gossip website RadarOnline.com, he said he felt "sick" after giving a sample of his DNA on the show.
Despite her mother Kristi Horn insisting she find out for certain if Michael is her father, Ashley told the show: "I don't want to be part of the Lohan trainwreck."
She also attacked Michael for refusing to acknowledge her in the past.
She said: "What gives you the right to tell me that the kids have a right to disown me. What made you say that to me? How can you keep lying?"
Lindsay cut Michael out of her own life after he tried to stage an intervention to get her to return to rehab last month.
The troubled starlet was said to have been pursuing a restraining order to stop her father from constantly interfering in her life but so far no legal documents have been filed.