The complete stotra, translated into English, is available on the Hindupedia.com website.
Quoting from there:
Dathathreyam Mahathmanam, Varadam Bhaktha Vathsalam,
Prapannarthi haram vande, Smarthrugaami Sanovathu., 1
Salutations to Dathathreya who is a great one, Who loves and blesses his devotees, And who destroys all worries of those,
Who always remember ...
According to texts, wherein the birth of Sri Dattatreya was mentioned, Anasuya and Atri are his parents.
Anasuya and Atri appear in the fag end of Ayodhya Kanda of Valmiki Ramayana. However, Sri Dattatreya was not even mentioned therein.
So the answer is Sri Dattatreya was not mentioned in Valmiki Ramayana.