B.G 3.19

tasmādasaktaḥ satataṁ kāryaṁ karma samācara। asaktō hyācaran karma paramāpnōti pūruṣaḥ ॥19॥

Therefore, practice the activities of duties without expectation of result. It is he who practices duties firmly without expectations that attains the highest good.

Gīta Tātparya 3.19

Perform duties with equanimity is the conclusion. Arjuna belongs to the category of beings eligible for liberation based on testimonials from Mahabharata. To say he belongs to the lower category is not appropriate (with reference to Advaita interpretation)

yasmādamuktasya kāryamastyēva tasmādasaktaḥ। asakta ācarannēva yasmāt paramāpnōti। muktasyaiva kāryaṁ nāsti ityēvakārārthō'pi yastu iti tuśabdēna avagataḥ। "tasmāt karmasamācara" ityupasaṁhāravirōdhaścānyathā।

For one who is not liberated there are even activities. Therefore, he should become 'asakta', i.e. devoid of curiosity or expectation. By practicing only without expectation, one attains the Supreme. Only the liberated do not have activities is indicated by using the words 'ēva', i.e. 'only', and by the word 'yastu', i.e. 'he who' (3.17 'यस्त्वात्मरतिरेव'). "Therefore perform duties with equanimity" is the conclusion. Else, (if interpreted as no need to perfrom action), there is opposition.

"brahmaniṣṭhā brahmaratā brahmajñānasutarpitāḥ। pāṇḍavānāṁ ca muktānāmantaraṁ kiñcidēva hi॥"

"Being steadfast in the Brahman, delighting in the Brahman, and contented in the knowledge of the Brahman, indeed there is little difference between the Pandavas and the liberated."

iti bhaviṣyatparvavacanācca na arjunasya amukhyādhikāritā। ātmaratirēva syādityēva śabdēna muktānāmēbhyō viśēṣō darśitaḥ। ēṣāṁ kadācid duḥkhābhāsasyāpi bhāvāt ॥19॥

- thus is the statement from "Bhavishyad-Parva", indicating Arjuna does not belong to an ineligible category. The usage of words such as 'ātmaratirēva', i.e. 'one who delights in the lord', and 'syat', i.e. 'perhaps', specially shows they are addressed to those who are eligible for liberation. Even among them, sometimes misery is experienced.