Bull and bear fights were a popular form of entertainment for the miners and prospectors of California during the mid 19th century. The preferred contest was between a Grizzly Bear and the Spanish bull of Mexico.
The animals would be placed within a circular pit, and the nose of the bull cut so that the blood would trickle into its mouth and nostrils and enrage the bull. The fight was to the death, and usually one-sided, with organisers (less willing to sacrifice the harder-to-come by, more valuable bears) sawing the horns off the bulls beforehand.
These contests had come to an end by the 1860s with the grizzly bear population hunted into near extinction.
Fights involving lions would have been rarer, given the difficulty in obtaining a lion, but a NY Times article dated April 12, 1898 shows that the spectacle was still taking place in Mexico towards the close of the 19th century. Click here.