To me it's rather obvious. The fly made it into our world through the wardrobe only to languish on the hot windowsill.
As Lucy drew close, he gasped out, "Bring the others! Come quickly!" But she did not hear his thin, high, buzzy voice
I disagree EveningStar. Thye fly was sent through the wardrobe by Jdis herself to assure that no one passed into her domain. But then he found the environment of England to be so different than that of Narnia that he became sick from even the most common bacteria that English flies have and succumbed before he could warn Lucy not to enter.
"Was there dust? I can't remember quite clearly, but I don't think there was a noticeable layer of dust there. I WANT DUST!!!! XD"
NalsA-AslaN, now that you mention it, there was no dust. The dust cover that Lucy removed from the wardrobe was clean, implying that it had to have been washed and put back on the wardrobe recently. Had the room been abandoned, when Lucy took the cover off the wardrobe, it should have set up a lot of dirt and dust.
MrBob