Lith grease is not exactly a liquid.  It does not flow into
the small gaps between the moving parts.
Go to the auto parts or hardware store and get a spray can of
chain oil.

Look again Ed - at the hinge.  You'll see a round roller about the size of a
dime, or so that is part of the hinge.  Lube it and make sure it rotates
when you open and close the door.  It will probably take a bit of lube and
then opening and closing to get it to rotate well.  If you don't get that
disk rotating you'll never get past the squeak.

Tr squirting the little rollers that (should) roll against the springy metal
bar. Hard to explain.

The door has developed an irritating squeek when opening and closing.
I've sprayed lithium grease on all the places on the hinge where metal
moves
against metal, but no help. Any ideas what's causing the squeek and
how to fix it?

TIA

Ed