The victim, aged in her 70s, remains in a serious condition in hospital after she was found with a head injury on the cycle path close to Ovangle Road, near Asda, at 7.30am.
She had been walking her dogs when she was attacked, say police, who have since arrested a 32-year-old man from Heysham on suspicion of assault.
He remains in custody but has not been charged with an offence at this stage.
Last night (Thursday, April 7), police also appealed for help in identifying a man who might have witnessed the assault. Detectives say he has now been identified and has spoken to officers.
A police spokesman said: “We were called at around 7.30am on Tuesday (April 5) to reports the woman, who is in her 70s, was found with a serious head injury on the cycle path close to Ovangle Road.
“She was later taken to hospital for treatment and is in a serious condition.
“Following further enquiries a 32-year-old man from Heysham was arrested on suspicion of assault and remains in custody.
“While we have made an arrest, we are continuing to conduct a number of enquiries and are working hard to establish exactly what occurred.
“We are continuing to appeal for information and we would appeal to anybody who was using the cycle path, close to Asda, between 7.15am and 7.40am and who saw anybody else on the path or saw anything that seemed suspicious to please contact us.”
Det Insp Andy Ellis added: “We know the cycle path is busy with commuters and dog-walkers at this time of the morning so we believe there will have been people in the area who saw something potentially significant.
“Whatever you know we would ask you to get in touch straight away.”
The attack is the latest in a spate of criminal incidents on the Lancaster to Morecambe cycle path in recent months. In response, concerned residents have launched a petition calling on the Council to install CCTV along the route to improve safety.
"A change must happen,” said Luke Edmondson, who started the petition, which you can view here.
"You should never be scared to leave your own home. And that change has to be better lighting and CCTV cameras to make people feel safe walking on their own down that route.”
Lancaster City Council have been approached for comment.
Anybody with information should contact police on 101, quoting log 212 of April 5.