Not sure why this is happening, but you have two options. First is to export to shapefile then import the shapefile to your spatialite database or you can create the grid in Spatialite itself.
First you need to know the extent you want, if you want to use a shapefile just go to the metadata section of its properties and you will find something like this:
xMin,yMin 140.999,-37.5049 : xMax,yMax 153.638,-28.1573
Alternatively if you want to just specify by using the map canvas, do it in the map composer where you can find the extent coordinates in the item properties.
Now that you have the two extent coordinates you can use the following set of queries in Spatialite:
Create the table
CREATE TABLE grid (id INTEGER NOT NULL PRIMARY KEY AUTOINCREMENT);
Add geometry column
Create the grid
INSERT INTO grid (geom) SELECT ST_SquareGrid(SetSRID(BuildMBR(140.999,-37.5049,153.638,-28.1573),4283),0.1) as geom
The BuildMBR function turns those two coordinates into a rectangular polygon which is the extent you are looking for. It is important to ensure you use the same SRID in the SetSRID function as you do when you add the geometry, otherwise it will fail. Finally the just change the grid size, noting that the units will be that of the coordinate reference system you use.