Standard kanji spelling. 獅子 means 'lion', and 鼻 means 'nose', referring to a nose shape resembling a lion's.
しし鼻
Mixed kanji-kana spelling. Less common but still used.
Etymology
Compound of 獅子 (shishi, 'lion') and 鼻 (hana, 'nose'), referring to a nose shape reminiscent of a lion's nose. The reading ししばな is a straightforward combination of the two words.