I was gonna say something like Criminal Minds, but on second thought, I think L would want to escape from all that crime stuff, and watch a cooking show where they make lots of sweets. I don't watch those kind of shows myself, so I can't name any names.
i think the exact same thing as you. since he is the worlds best detective (and 2nd and 3rd i think) he mite watch those crime shows like:
*law and order
*maybe some cartoons
*oh and just a thought but maybe "say yes to the dress" (a show where people try on wedding dresses)
*oh and the security camera ;)