Compile in delphi mode ? But that it works in Delphi is sheer luck, fat chance that it only delivers a nice GPF.
This desciption is a bit confusing... TStringGrid, TDrawGrid, TDBGrid? Which type is grdMyStringGrid? You probably only did not do the type-cast correctly. "ColWidths" is introduced as protected by the most elemental grid, TCustomGrid, from which all Lazarus grids are derived.
TDrawGrid(grdMyStringGrid).ColWidths[1]:= 650;
... because the property TStringGrid.ColWidths was protected - therefore impossible to modify - while the property TCustomDrawGrid.ColWidths (from which the TDrawGrid inherits) was published. Hence the "over-typecasting".
[...]
"TDBGrid and TDrawGrid are not related"