Adding Nodes to Linestrings at Overlapping Points with Polygon Layer in Spatialite

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I have two Spatialite tables.

1. A table called 'lines' which contains a PK column called OGC_FID and a LINESTRING column called GEOM.
   
   
2. A table called polys which contains a PK column called OGC_FID and a POLYGON column called GEOM.
   
   

How do I update the 'lines' table GEOM so that the intersection points with any POLYGONS in the polys table are added to the LINESTRING geometries?

(Preferably using SQL queries only. Temp tables are fine) (Postgis answer acceptable)



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