Canto 2 -
Ayodhyā-kāṇḍa
Chapter 53: Rāma Requests Lakṣmaṇa to Return to Ayodhyā
Text 2.53.31

न च सीता त्वया हीना न चाहमपि राघव।
मुहूर्तमपि जीवावो जलान्मत्स्याविवोद्धृतौ॥

na ca sītā tvayā hīnā na cāham api rāghava
muhūrtam api jīvāvo jalān matsyāv ivoddhṛtau

na ca = neither; sītā = Sītā; tvayā hīnā = without You; na ca = nor; aham api = I; rāghava = Rāghava; muhūrtam api = for even a muhūrta; jīvāvaḥ = can live; jalāt = of water; matsyau = fish; iva = like; uddhṛtau = taken out.

Rāghava, neither Sītā nor I can live without You for even a muhūrta, like fish taken out of water.

This is Lakṣmaṇa’s response to Rāmacandra’s request in text 16 that He go to Ayodhyā the next day.

Text 3.15.6 will note that Lakṣmaṇa will surrender unto Lord Rāmacandra and beg Him for service in the presence of Sītā-devīsītā-samakṣaṁ kākutstham idaṁ vacanam abravīt: “Lakṣmaṇa spoke the following words in the presence of Sītā-devī.” Therefore, the statement that Sītā-devī and Lakṣmaṇa won’t be able to live without Rāma implies that if Lakṣmaṇa does not attain the result of surrendering unto Rāmacandra, Sītā will also not [attain the benefit of being a mediator between Lakṣmaṇa and Rāmacandra].

Api can mean “if” and this indicates that if Lakṣmaṇa and Sītā were to live [in Rāmacandra’s absence], it would only be for a short while like fish taken out of water. Just as fish taken out of water survive as long as they are in touch with water and die in the absence of water, similarly Sītā-devī and Lakṣmaṇa would live, Lakṣmaṇa states here, as long as talks about Rāmacandra occupy their hearts. This will be stated in Sundara-kāṇḍa (Canto 5):

na cāsya mātā na pitā ca nānyaḥ
snehād viśiṣṭo ’sti mayā samo vā

tāvat tv ahaṁ dūta jijīviṣeyaṁ
yāvat pravṛttiṁ śṛṇuyāṁ priyasya

“O messenger, neither His mother nor His father nor anyone else is equal or greater in affection to Him. So I desire to live as long as I can hear about my beloved husband.” (Rāmāyaṇa 5.36.30)