Ecila Henderson chased 69-year-old Rosemary Armstrong from her flat in Pokesdown, Bournemouth, in August 2010 and stabbed her 22 times.
Ms Henderson, now 45, admitted manslaughter on the grounds of diminished responsibility and is detained in a mental health unit.
An inquiry later criticised the care she received from her health trust.
Ms Henderson had been under the care of Southbourne Community Mental Health Team, part of Dorset Healthcare University Foundation Trust.
One of the core criticisms of the trust was its failure to act quickly when a health worker reported Ms Henderson's condition had deteriorated significantly. The trust admitted liability for negligence.
Ms Henderson is seeking damages for the psychiatric harm suffered because of the killing and her loss of liberty.
The case, being heard in the High Court, must decide whether the claim contravenes the law which prohibits a person from recovering damages for the consequences of their own illegality.
Ms Henderson's counsel, Nicholas Bowen QC, said his client had an acute sense of loss which went beyond feelings stemming from ordinary bereavement and any efforts to address the grief was likely to cause further deterioration in her condition.
A woman with paranoid schizophrenia who killed her mother is suing a health authority for more than Â£300,000.