Lindsay Clancy is taking one more swing at avoiding a second trial ... asking a judge to find her not guilty after her murder case ended in a mistrial.

According to court docs, obtained by TMZ, Clancy's attorney Kevin Reddington is asking the judge to find her not guilty by reason of lack of criminal responsibility ... arguing prosecutors didn't prove she was legally responsible and in her right mind when she killed her three children.

The filing notes 11 of the 12 jurors were prepared to find Clancy not guilty by reason of lack of criminal responsibility before the jury deadlocked ... with one juror holding out.

Reddington argues all six forensic experts agreed Clancy was suffering from a serious mental illness at the time ... even though they differed on the exact diagnosis.

Her team says prosecutors still had to prove she understood the wrongfulness of her actions or could conform her conduct to the law ... and they claim the evidence fell short.

The defense says this isn't simply about turning the 11-1 split into a not guilty verdict ... it wants the judge to independently rule the evidence was legally insufficient to convict her, and she should be found not guilty.

If the motion is granted, the filing says it would amount to an acquittal and block prosecutors from retrying Clancy.

Her lawyers want the motion heard at a September 29 court hearing.

Stay tuned ...