Which is the series "Lost Sheep" of which plush doll Subaru Konoe is fan of?
I believe the '"Lost Sheep" series of plush dolls' is a line of toys that exists only in the Mayo Chiki universe, something like gashapon vending machine toys. (If I recall correctly, the Lost Sheep toys are larger and come from a crane game machine, though.)

Toys like this are fairly common in anime and manga since the characters are often teenagers who spend time in game centers, and they're quite common and ubiquitous in real life as well. From the Wikipedia article on Gashapon:


  Gashapon toys are often licensed from popular characters in Japanese
  manga, video games or anime, or from the American entertainment
  industry. These highly detailed toys have found a large following
  among all generations in Japan, and the trend is filtering to the
  world, especially among adult collectors. It is not uncommon for sets
  marketed specifically for adults to feature risqué female figurines.


(By the way, if you go through to the original article, do not click on the citation for that last sentence unless you are alone in a dark room, preferably about forty miles from the nearest civilization.)