It was there that officers discovered the body of a woman under the M50 toll plaza bridge, Dublin Live reports.
Police then rushed to a nearby house where a seven-month-old baby was found unresponsive and died at the scene shortly after.
Officers treat the incident as a family tragedy and are not looking for anyone related to the incident.
Lucan’s detectives found no signs of violence or evidence of violent death when they conducted a forensic examination of the house.
A police spokesperson said: “The Gardaí (Irish police) are investigating the circumstances surrounding the discovery of a woman’s body on Lower Road, Strawberry Beds, Lucan, Co Dublin and the unexplained death of a little boy in a house in Lucan Co. Dublin on October 22, 2020.
“At approximately 3:45 am on October 22, 2020, following reports of a pedestrian seen acting suspiciously at the M50 bridge (toll), Gardaí discovered the body of a woman in Lower Road, Strawberry Beds.
“Following this incident, Gardaí went to a house in Lucan where a 7 month old boy was found unresponsive. He was pronounced dead at the scene shortly after.
“An incident room was set up at Lucan Garda station and a technical examination of the scene took place. The coroner and the state pathologist’s office have been notified.
“The child’s body has been taken to Crumlin Hospital and the woman’s body has been taken to the town morgue where post-mortem examinations will be performed.
“The results of the post-mortem examinations will determine the course of the Garda’s investigations.
“At this point, Gardaí investigators are treating these incidents as a family tragedy and are not currently looking for anyone else in connection with the deaths.
“No other information is available at the moment. Investigations are ongoing. “