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Lillia was found seriously wounded in Fountain Lane, Lincolnshire, this Thursday 28 July.
The man in question was arrested today, 30 July, after two other people were arrested and released without charge earlier this week.
Shortly before the arrest, police were said to have cordoned off Thorold Street, just a five minute walk from where Lillia was found.
The arrest came after the police previously issued CCTV footage of a man they wanted to locate in relation to the case.
Lincolnshire Police confirmed the arrest: "Officers detained the man in the Boston Central Park area at around 2.45pm today (July 30)."
An investigation is still underway, with the police noting: "There will continue to be a significant police presence in the town while our investigation progresses.
"We are still encouraging anyone with information to contact us. You can do so via the major incident portal."
According to the police force: "The arrest follows a combination of intelligence and information supplied by several members of the public. We’d like to thank everyone for their assistance as we continue our investigation. We are not looking for anyone else in connection with this incident."
Chief Superintendent Martyn Parker added: "Our officers have been working round the clock on this investigation, and the public’s help may prove crucial.
"These are very clear images of a man we want to speak to, so I’d urge anyone with information to get in touch with us. If you see him, do not approach him but immediately call 999.
"This is a particularly tragic case and I’d like to reassure the public that we have a huge amount of resources dedicated to the investigation.
"We continue to provide support to the family of Lilia, as they grieve following this unimaginable loss."
The police chief went on to add that: "We are in a very sensitive stage of our investigations having just arrested a 22-year-old male.
"Please allow my officers the time and space to conduct their enquiries and continue their investigations."
Flowers and candles have been left where the incident occurred, Lillia was said to have been playing with her younger sister at the time.