Answer

In Jain tradition, the Tirthankar during the Ramayana period is generally identified as Lord Munisuvrata, the 20th Tirthankar. ( jainworld.jainworld.com)

Explanation

Jain sources place Shri Rama, Lakshmana, and Ravana in the same era as Munisuvratanatha. Jainpedia specifically notes that the Ramayana characters lived at the time of the 20th Jina. ( jainpedia.org)

Takeaway

So, the short Jain answer is: Munisuvrata Bhagwan. ( jainworld.jainworld.com)