Det Ch Insp James Entwistle of West Yorkshire Police said: “After extensive inquiries into Mr Bevan’s death we are now treating this as a murder.
“We are seeking to establish the full circumstances and as part of this continue to question three men in custody.
“His family are being kept updated as the investigation progresses.”
Bevan inflicted “catastrophic” brain injuries on the toddler in a “brutal” assault in her family home, his sentencing hearing in 2023 was told.
Lola was attacked on the night between 16 and 17 July 2020 while she was in Bevan’s care, and was left with 101 surface injuries on her body.
The judge, Mr Justice Martin Griffiths, described Bevan’s actions as “an assertion of superiority over the only person he could feel superior to – a helpless child”.