What does Clio's Lamp mean? When people refer to the lamp, what does it signify?

My opinion is that this is a mixed metaphor.  Clio is the muse of
history, but was not traditionally depicted with a lamp, but rather a
scroll or something similar.

"The Muse Clio"
Circle of the Muses
http://www.eliki.com/portals/fantasy/circle/clio.html

The methaphor "Clio's lamp" in the first paragraph of this page is
apparently meant to evoke the continued inspiration of the muse of
history.

"The Future of World Conflict: A Review of Huntington’s Clash of
Civilizations", by Jonathan M. Acuff (Prof. Jordan, GFIR 506, 29 July
1998)
Jonathan Marshall Acuff
http://www.geocities.com/wmhistory1993/CLASH.html

But "Clio's lamp" is not a common metaphor.

I would post this as an answer, except someone might be able to find
an actual association between Clio and lamps that I have not found. 
If you decide you would like me to post it as an answer, I would be
happy to do so.

I agree with justaskscott. Clio does not carry a particular lamp. I
believe this phrase refers to keeping history alive and remembering
the lessons learned from the past.

- Hammer