In Buddhism, Ramayana is known as “Dasarata Jataka” meaning Tale of Dasarata (King Dashrath, father of Rama). It is claimed that Buddha came from the Ikshvaku clan (of Rama). (ref Fang, Liaw Yock (2013). A History of Classical Malay Literature. Jakarta: Yayasan Pustaka Obor and ISEAS. ISBN 978-979-461-810-3.)
The Dasharatha Jataka is one of the stories of the past lives of Buddha as a Bodhisattva. Here he explains to a householder why he must overcome the grief of the demise of this father. Dasaratha, Rama, Lakkhana (Laxmana), Sita & Bharat, all appear in this story. (Ref/Download https://www.scribd.com/document/281051975/The-Dasaratha-Jataka)
Rama (called Rāmapaṇḍita in this version) was the son of Kaushalya, first wife of Dasharatha. Lakṣmaṇa (Lakkhaṇa) was a sibling of Rama and son of Sumitra, the second wife of Dasharatha. Sita was the wife of Rama. To protect his children from his wife Kaikeyi, who wished to promote her son Bharata, Dasharatha sent the three to a hermitage in the Himalayas for a twelve-year exile. After nine years, Dasharatha died and Lakkhaṇa and Sita returned; Rāmapaṇḍita, in deference to his father’s wishes, remained in exile for a further two years.
Rāmapaṇḍita is said to have been a previous incarnation of the Buddha, and Sita an incarnation of Yasodharā. Ravana appears in other Buddhist literature, the Lankavatara Sutra.