Question
Why is Lakshmana not considered an incarnation of Vishnu?
Answer
In Valmiki Ramayanam BalaKanda it is mentioned that all the 4 sons born for Dasaratha are incarnations of Vishnu in various proportions.
अथ लक्ष्मणशत्रुघ्नौ सुमित्राऽजनयत्सुतौ।।1.18.13।।
वीरौसर्वास्त्रकुशलौ विष्णोरर्धसमन्वितौ।One fourth of Vishnu manifest. Sumitrá too a noble pair, Called Lakshman and S'atrughna, bare, Of high emprise, devoted, true, Sharers in Vishnu's essence too.
The above text is relevant for Lakshmana's birth and it is clear that he is considered incarnation of Vishnu.
chapter 19, Bala Kanda of Ramayana
In Srimad Bhagavatam, Skanda 9 Chapter 10, it is mentioned that all four sons of Dasharatha are incarnations of Lord Vishnu.
Thanks to @SwiftPushkar for giving the Bhagavatam reference.
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