Part of the danger of just copying and pasting whatever you find from a Google search, is unless you actually know or research what you find, you could be incorrect.
Not only did you lift something from the "Conservapedia" website without providing a source, the list is inaccurate. I'm surprised you of all people would post such inaccurate information. I thought you were better informed than this!
I didn't go through every name, so there are likely others which are incorrectly on the list. Interestingly, Sonny Bono is not on this list.
Joe Lieberman - not a conservative! Dude was a socially liberal Democrat and remained so. He didn't cross over. Sure, he supported John McCain and was a fiscal conservative and military hawk, but he wasn't a liberal to conservative story.
Kirk Cameron - Atheist at 17, no record of being a liberal.
Sandra Cano - Do you know who she is? There's no record of her being a liberal who then switched to conservativism.
Antony Flew - No record of him being a liberal. He was noted as being a Libertarian-leaning conservative.
Sidney Hook - He embraced Communism in his youth, and though later rejected it, he was noted to be a pragmatic social Democrat. Some claim he was a Fellow at the Hoover Institute; however, the Hoover Institute website doesn't have him listed as a Fellow.
Lisa Miller - Know her? No record of her changing from a liberal to conservative either.
Zell Miller - Conservative Democrat. Stated he would be "Democrat" until I die. Began as a conservative southern Democrat, remains a Democrat - having supported a Democrat in the 2012 campaign.
http://www.conservapedia.com/List_of_former_liberals