Hi AnneMack,
Sounds like you have a whole deal of problems with Mavericks, I had a few glitches with Mavericks after the first install, most of them sorted out by doing a clean reinstall of Mavericks as recommended by Apple support when I called them
On my iMac mid 2011 I don't have the option of locking any energy saver options in Mavericks, it doesn't look like it should be an option
On my original post the question was the iMac not going to display sleep and computer sleep at the times I had set
I have discovered on my machine that since 10.9.2 if you have screensaver working then display sleep et cetera will not work accurately, sometimes works sometimes doesn't, if you turn screensaver to "never" then display sleep et cetera seems to always work
I think it is all a bit fragile, and will get sorted in time, but might be worth thinking about a clean reinstall of Mavericks for you
Good luck