One observation with applying the oil to the "ball bearings" on the hub/spindle of the fan ... I swabbed onto it something called WD40 which oils locks etc but the problem came back after about 40 hours or so and that horrible grinding noise returned - I dunno why, whether I didn't apply enough or made sure the oil penetrated the internals etc.
In the end I had to replace the fan manually myself .. and to this day the vaio laptop 13 still works ... I did use new thermal paste though so that's worth considering also. Replacing the fan aint too bad, there's a video on you tube that shows you how to do it, I got the fan from China off ebay shipped to Europe but I recall that the hardest part was pulling the case off the vaio... do it with CARE.