The Lighstspeed platform is described on:
and is OAuth Code Grant Flow-based, including Swagger/Open API.
There is also a key / token-based approach as described on:
For Lightspeed Restaurant K-series: see SQL/Power BI connector for Lightspeed Restaurant K-series.
For Lightspeed Restaurant L-series: see SQL/Power BI connector for Lightspeed Restaurant L-series.
For Lightspeed Restaurant U-series: see SQL/Power BI connector for Lightspeed Restaurant U-series (Upserve).
No links for Lightspeed R-Series and O-Series.