No, they are not interlinked in Jain Dharma.

In Jain tradition, Parshvanath Bhagwan’s lanchan is the serpent (snake) because it is associated with a special incident in His life, where the Naga king Dharanendra protected Him. The snake symbol therefore represents that connection and His compassionate, protected state.

The snake associated with Shiv Bhagwan belongs to a different religious tradition and has a different meaning there. In Jainism, we do not treat that as connected to Parshvanath Bhagwan’s lanchan.

So, from the Jain viewpoint:

• Parshvanath Bhagwan’s snake symbol is specific to Jain tradition
• It is not linked to Shiva’s iconography
• Similar symbols in different traditions do not mean the same identity or doctrine

The lanchan of a Tirthankar is mainly used to recognize that Tirthankar and to remember a sacred event or symbol connected with that life.