Why did Shiva wear lion skin clothes?
Lord Shiva himself is Parabrahma. That’s why they like to remain in their true form i.e. naked. But he accepted Sri Hari’s request and accepted Baghambar or lion skin as his clothes.
This story is related to Narasimha avatar of Lord Vishnu. To protect Prahlad, Shri Hari took the incarnation of Narasimha and killed Hiranyakashipu with his claws. But angry with the atrocities on the devotee, Narasimha became determined to destroy the entire creation. He rejected the prayers of all the gods and even Brahmaji and Lakshmi.
Then Mahadev sent his Gana Veerbhadra to protect the creation. Veerbhadra tried to remind Vishnu of his true form in the form of Narasimha. But the disillusioned Narasimha did not listen.
Then Mahadev took the incarnation of Sharabha to protect the world. Which was the combined form of Veerbhadra, Garuda and Bhairav. He had eight powerful claws and powerful wings.
In the form of Sharabha, Veerbhadra was situated in one wing and Mahakali in the other wing, Bhairav was situated in the head of Lord Sharabha and Sadashiv in his beak and Shiva in the form of Sharabha held Lord Narasimha in his claws and flew into the sky.
Shiva wrapped Narasimha in his tail and started hitting him with his beak on his chest. Then he tore her navel with his claws.
Narasimha’s attachment was destroyed. His glory separated and appeared in the form of Mahavishnu. He requested Mahadev to honor Narasimha by accepting his skin as his clothes. After this, the great Pashupati Shiva wore that skin as his clothes and seat and revealed his charming form in the hearts of the devotees.