Mr Lali, who is in his mid 50s, faced Lamu Principal Magistrate Allan Temba by video link on Tuesday, following his arrest over Tecra's death.
The court document says that within that period, the DCI will take statements from witnesses, analyse the scene, and conduct a postmortem and the forensic analysis of phones, CCTV footage and/or
It was established that Tecra died from head injuries sustained in a fall on the stairs of a private house in which she was staying with Mr Lali in Shella, Lamu.
Omar Lali, boyfriend of Keroche Breweries' Tecra Muigai Karanja who died on Saturday, will be detained 21 more days for police to complete the probe into the death.
Mr Lali, who is in his mid 50s, faced Lamu Principal Magistrate Allan Temba by video link on Tuesday, following his arrest over Tecra's death.