Actually, that "Lion Dog" bit is often debated between Pekingese and Shih Tzu. I just talked with my mother and she translated the words for me.
Shih Tzu (she said) literally means 'very pretty' or 'beautiful'. The Crysanthemum bit is undebated, however. The beard obviously has some connection with the crysanthemum flower. However...

Lion Dog- When Chinese people refer to 'Lion', they usually refer to the two Lion statues in Beijing/Peking (whatever you'd like to call it). As you know, Beijing/Peking houses many palaces and priceless statues and is a greyt area of ancient culture. There are two very famous Lion statues over there, and she said, literally, when people refer to Lion, they refer to Beijing/Peking. With that in mind, she said firmly that Pekingeses are Lion dogs. She says that without English, Chinese people called Beijing dogs/Peking dogs/Pekingeses, Lion Dogs. The word Peking Dog or Pekingese is an English translation, and she says that traditional Chinese folk call Peking Dogs/Pekingeses, Lion Dogs. Besides that, I've seen many many statues of lion dogs (often placed in front of the home or palace to enforce good luck and detract bad luck/spirits). Trust me when I say, 99% of those statues have NO beard. Their build is similar to that of a Peke (bulky, pear shaped, bowed front legs, short, squat, etc.). If you also look at an old photo of a Pekingese, you'll see that it resembles more of a Tibbie than a modern Peke. Compare that old Peke photo with a statue of a Lion Dog, and you can automatically see the similarities. Anyhow, just my op. By the way, I was told the Shih Tzu was a Lion Dog and have asked others and was then told Pekes were Lion Dogs. After doing a bit of research, I can't say I'm sure, but I think the Pekingese is still valid to be labeled Lion Dog.