The bolded passage is the rising action.
In a narrative, the rising action is the event, or series of incidents, which come directly after the exposition and before the climax. Its purpose is to set up suspense in the plot (in this fable, you can sense the tension in phrases like "he seized it with his paw and was about to kill it"). It is usually composed of character decisions and personality traits (here, the mouse's cunning and the lion's arrogance).