Lakshmaṇācala means the hill (acala, mountain) of Lakshmaṇa, the younger brother of Bhagavān Rāma. It is a sacred hill and a tīrtha, named in the Nārada Mahā Purāṇa.

The Uttarārdha of the Nārada Mahā Purāṇa places it among the great Śaiva tīrthas of the south and west of Bhārata. These are told by Vāsu to Mohinī. Here Lakshmaṇa did tapas (austerity) and worshipped Bhagavān Śiva, and the place became sacred for all time.

Place in the Purāṇa

The Uttarārdha lists Lakshmaṇācala between Gokarṇa (Chapter 74) and Setu (Chapter 76). The name ties the hill to Lakshmaṇa, the younger Rāghava, who left his mark here through tapas and worship. (Nārada Mahā Purāṇa, Uttarārdha, Chapter 75)

Lakshmaṇa’s tapas and worship of Bhagavān Śiva

At this spot Lakshmaṇa worshipped Bhagavān Śiva and did tapas. The Purāṇa says Bhagavān Śiva was pleased with his devotion, and a liṅga was set up here. The merit of Lakshmaṇa’s own devotion fills the hill. It brings spiritual good to all who visit. (Nārada Mahā Purāṇa, Uttarārdha, Chapter 75)

Merit of the visit

Darśana (sacred sight) of Bhagavān Śiva at Lakshmaṇācala, and snāna (a holy bath) in the tīrtha there, give:

The merit of an Aśvamedha yajña.
The blessings of both Bhagavān Śiva and Bhagavān Rāma, through the link with Lakshmaṇa.
Freedom from the pāpa (sin) built up over many births.

Sources

Nārada Mahā Purāṇa, Uttarārdha, Chapter 75