screenshot?

I didn't get a lot of response to this basic, yet very important question, however, I think that I, (a mere novice), have stumbled onto a solution.

Since my repositories would not update by using the "Updates" button, I decided to take the long way around and use "Synaptic".  It also would not update the repository cache, BUT it did show me where it was hanging up.  In my case, it was:  

http://ppa.launchpad.net/vokoscreen-dev/vokoscreen/ubuntu/dists/precise/main/binary-i386/packages

From what I can deduce, if the repository cache update process cannot find any of the repositories it's looking for, it stops right there,  and you are done.  It will not skip over the one it can't find and keep going, nor will it let you at least update the apps that it has found up to that point.  It's a pass/fail, all-or-nothing process.  (Maybe 'they' should fix this, huh?) 

So what did I do?  In Synaptic, I clicked on Settings > Repositories > Other Software (tab), and unchecked the offending repository.  Then I backed out and tried to reload my repository cache, Voila! It worked.  I can now update the repository cache either in "Synaptic" or by using the (easier) "Updates" button.

I hope that this info helps someone.  As I said, I am a novice, so if any (or all) of this stuff is wrong, or incorrectly stated, I'm sorry.  With no support, I did the best I could, and I found a solution which worked for me.  But, lest any of this sounds too negative, I do still love LXLE.

OK, I'm two years late in responding.  I can be a little slow, too.  I hope that M-I-L thing went OK  for you.  Some mothers-in-law can be nearly impossible to pick up.  BTW, thanks for the refund.  I spent it on beer.