Lincolnshire Police said the 22-year-old was detained in the Boston Central Park area at around 2.45pm on Saturday.
It comes after the force released four CCTV images of a man they sought to identify, and several members of the public came forward with information.
The man is being held in custody, and while police are not looking for anyone else in connection with the incident, officers will continue investigations in the town.
In a statement at 4pm on Saturday, Chief Superintendent Martyn Parker thanked members of the public who had aided the inquiry, and urged anyone else with information to contact police.
He said: ‘We are still encouraging anyone with information to contact us and you can do so via the major incident portal, of which the details are on our website.
‘Once again, I would like to personally thank you for the support you have shown from members of the public and from the media. ‘Your support is very much appreciated.’
Lillia was found on Fountain Lane in Boston at about 6.20pm on Thursday. She had reportedly been playing with her younger sister on the street just yards from an office where their mother was working at the time.
The girls had a hula-hoop, and a toy pram was left at the scene, according to local people. A resident from the area told the Telegraph: ‘The little girl was playing in the street with her younger sister when it happened. They had some toys out.
‘I’m sure her mum wouldn’t have been far away as she always checked on them. She was a very quiet girl, and I just can’t understand it. ‘I didn’t see what happened, but we were told they (police) were looking for footage of a man running away.’
Jurate Matulioniene, a family friend and chairwoman of the Boston Lithuanian Community, told The Times: ‘Lillia was a beautiful angel, she was quite quiet and loved dancing. ‘The family used to come to all of our community events and they would always stay late to help clear up.
‘I have spoken to the mum and asked for her account details because we want to do a fundraiser but she would not accept it.’ Police have altered the spelling of Lillia’s first name in their latest update.