Personally didn't try Blender nor Lightwave 3D but companies that use the FBX currently (including ours) use Maya and 3DS Max which both work.
Also keep in mind that you need to have textures on all objects etc. Genome2D may crash if there is for example geometry without texture etc. atm.
If you are working with Haxe directly you can debug it quite easily and let me know, if you are using the SWC just send me the FBX and I may point you to the problem once I have time to check it out.