Sorry this is slow. I recently joined the forums.
Your model had a couple "bad" surfaces in it. These were revolved surfaces making up half of the bottom bowl of the tulip shaped piece. Because it was made into a Block before the bad surfaces were fixed, the errors carries to the 6 instances of the block.
In Rhino, I deleted the instances of the blocks, and Exploded the remaining block. I have CheckNewObjects turned on so was notified of the bad object being added to the file. I ran SelBadObjects and one of the large polysurfaces highlighted. Next I ran ExtractBadSrf and the two surfaces highlighted. I inverted the selected and ran Hide to get the good objects off the screen.
Fixing the bad surfaces was easy, I extracted the trim curves and retrimmed the surfaces using the extracted curves. This technique works for 95% of bad surfaces. More techniques are covered in this FAQ: rhino:badobjects [McNeel Wiki]
I Joined the fixed surfaces back into the polysurface.
I did a double check by exploding the polysurfaces and Joining them again. No naked edges were found so the model was originally done accurately without any cheating.
See if this fixed version opens and heals better in SolidWorks now.
Lambent Assembly v4 fixed.zip 11.3 MB