Lisa had initially stayed in the area of Keratsini, 5.9 miles (9.5km) west of central Athens, with Greek friends.
She had told them that on 15 July she would go to Kypseli, where her “American friends” or acquaintances were.
Police sources said officers were looking to identify these individuals.
Her mobile phone was transmitting a signal and sending some messages a few days after her death.
On Wednesday, the Foreign, Commonwealth and Development Office (FCDO) confirmed they were providing consular support and were in contact with the Greek authorities.
First Minister John Swinney called it an “absolutely appalling case”, and said her family would be supported by the Scottish government and the FCDO.
Police Scotland said they were also providing support to Lisa’s family.