Hello,

It's not possible to achieve that directly with odoo.

To achieve your need you have to choose between the two ways:

    1- Develop an Abstract Model with all the treatment necessary to get data from odoo (Postgresql) and send it to Your external database (SQLite) then create a cronjob that calls the function of your abstract model.

    2- Use Data Replication Mecanisme: This method is completely independent of odoo and you have to implement it on Postgresql. For data replication, there are two architecture: Master To slave & Master To Master. Postgresql does not support Master To Master on its core and Master To Slave function in PostgreSQL is not convenient for your case. However, there are several tools that allow implementing different architecture and I recommend to use Bucardo (But you have to check first if it supports SQLite)

•     Please check this link for more information about Postgresql Data Replication and the different tools:
      https://wiki.postgresql.org/wiki/Replication,_Clustering,_and_Connection_Pooling
  

It depends on your need to choose which method is more convenient for you but I recommend using data replication.

Good luck.