Prosecutors said blood spatter evidence inside Lyons' van suggests the girl was stabbed there before she was discovered in the alley behind her father's home.
Lyons' attorney, Alan Blumenthal, said his client continues to maintain his innocence.
"We look forward to challenging the so-called scientific evidence in this case because as far as I can see now, that's the only evidence in this case," said Blumenthal.
There continues to be debate as to whether the young girl was sexually assaulted. Blumenthal said he's seen medical reports from the hospital where Mya Lyons died indicating that she was sexually assaulted and that DNA was recovered from her body. The insinuation is that the DNA evidence would clear the Richard Lyons.
Cook County State's Attorney Anita Alvarez said there was no evidence that the girl was sexually assaulted in the case, but that she'd suffered 10 separate stab wounds as well as multiple skull fractures and brain injuries.
"As prosecutors, we see violence rise up in many ways and in many forms and in our communities, but the inhumanity of a crime such as this is almost beyond comprehension," she said.
Richard Lyons also is being held on a $250,000 bond in connection with the sexual assault of a 15-year-old boy. Blumenthal said Lyons is maintaining his innocence in that case, as well.
Police arrested Lyons Tuesday after prosecutors said they have evidence directly linking him to the crime.