The problem you're seeing is that the object itself is still the square, blocky object you originally modelled. All pressing the Tab key does is tell lightwave to perform subdivision on the surface - this is only viewable within LW itself.
What you need to do is to actually freeze the mesh once it has been subdivided if you are going to export it to another object format.
If you are only going to work on the object within Lightwave itself, then simply save the object (which should save it in the native LWO format) rather than exporting it.
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