There is an auto-saving image. Your last rendered image is in a directory that you can set in the LuxBlend script, under the System Panel (the second path to fill). Your image is there !
You can also choose to continue rendering, while exporting the rendered image of the moment. Simply find the Copy-Paste button that laid on the right of the Play, Pause, Stop and Threads buttons (3rd row on the upper left corner of LuxRender User Interface).
Saving a .flm won’t give you an image, but will permits you to continue rendering later, reopening it.
Rendering times depends on scene complexity, on computer’s capabilities and rendering choices (picture size, samples, etc…) and so on, but it is often seen rendering times up to 10 or even more hours…