Well, that translation is far from being literal or even close to the original, the translator certainly took many liberties when translating the poem.
A better translation would be:
“Surely,” said I, “surely that is something at my window lattice; - Ciertamente, dije, ciertamente eso es algo en la rejilla de mi ventana.
Let me see, then, what thereat is, and this mystery explore-- Dejame ver, entonces, que allí hay, y este misterio explorar.
Regarding the conjugation of the verb "dejar", it's "dejadme" (or "dejame") because the original is "let me", so asking why it's "dejadme" (or "dejame") would be the same as asking why it's "let me", it's just the author's style.