Lamas was 20 weeks pregnant when she collapsed at home Feb. 9, and was rushed to the hospital where she underwent an operation to stop massive internal bleeding.
Lamas' second child with Richie died during the surgery. Lamas, who was briefly placed in a medically induced coma and suffered cardiac arrest, remains in the undisclosed hospital's intensive care unit.
Richie told TMZ he held his son a few days after he died and said a prayer for the child with hospital staff.
He also named the boy Rex Jagger Lamas-Richie, so the staff could fill out a birth certificate.
Richie told the celebrity news web site he was glad to see his son, but it was the hardest thing he has ever done.
Lamas married Richie in 2010. Their daughter Press was born in November 2011.
Lamas is the daughter of actor Lorenzo Lamas. She is known for her work on the soap opera "General Hospital" and in the reality TV shows "The Bachelor" and "Leave it to Lamas."