I'm not familiar with Chinese New Year. Though they only used dragons in that one. Whatever.

I know of the Chinese tradition of placing "guardian lion" sculptures at the entrance of buildings and the like, sometimes incorrectly referred as "Fu dogs". The lion is not native to China. This tradition first started during the Han Dynasty (206 BC - 220 AD) and its origin is disputed but apparently linked to contact with the west through Central Asia.

One possibility is that Chinese merchants brought lions through the Silk Road, or that foreign diplomats from the west gave the Chinese lions as gifts. Gifting exotic animals has a long history and lions have always been a popular choice. Sometimes the poor animals travelled really long distances in their lifetimes as they were just passed from one state ruler to another to another. Lions didn't live in Central Asia proper (i.e. Mongolia, West China and the former Soviet 'Stans) but they lived in Persia and India (a tiny population of wild lions still survives in India today).

The other possibility is that lion imagery came not from actual lions but as a by-product of Buddhism. Buddhism also enters China during the Han Dynasty, and does it through the Silk Road. Buddhism originates in India. Lions have a long history as symbols of authority in India. In fact, the modern emblem of India depicts three lions, modeled after the ones decorating a pillar erected by Emperor Ashoka around 250 BC. Ashoka ruled as far as Afghanistan (the place from where Buddhism entered China) and during his reign there were thousands of these pillars through his empire, inscribed with the laws edicted by Ashoka.