You may want to refer to this information, it shows the different types of integration that can be performed. Point-to-point integration (not using an ETL) is often a cause of stability problems as the connector must be coded to be compatible will all versions of software on both sides, it is very quick to implement but causes medium and long term maintenance issues.
We are in the process of releasing SaaS ETL and are happy to build a Litespeed POS connector, as we primarily only use APIs it bypasses the upgrade and stability issues.
Stay far away from lightspeed. it is a POS and not point of sale. I have been tyring to get it to work correctly with my magento for 2 months. Still not working correctly and it is impossible to get help.