What are assonance and alliterations in The Lake By Poe?

It seems you're asking about "The Lake" by Edgar Allan Poe, not "The Lake Isle of Innisfree" by W.B. Yeats. There isn't a poem titled "The Lake" by Poe, but there is one called "The Raven." If you meant to ask about "The Raven," here are some examples of assonance and alliteration:

Assonance (repetition of vowel sounds):

* "While I nodded, nearly napping, suddenly there came a tapping": The repetition of the short "a" sound in "tapping," "napping," and "came."

* "Deep into that darkness peering, long I stood there wondering, fearing": The repetition of the long "e" sound in "peering," "there," and "fearing."

* "Only this and nothing more": The repetition of the short "o" sound in "Only" and "more."

Alliteration (repetition of consonant sounds):

* "While I nodded, nearly napping, suddenly there came a tapping": The repetition of the "n" sound in "nodded," "nearly," and "napping."

* "Quoth the raven, 'Nevermore'": The repetition of the "r" sound in "raven" and "Nevermore."

* "Back into the chamber turning, all my soul within me burning": The repetition of the "b" sound in "Back" and "burning."

Poe was a master of sound devices and his use of assonance and alliteration adds to the poem's overall effect of mystery, suspense, and melancholy.

If you are interested in a different poem by Poe, let me know and I can look for examples of assonance and alliteration in that poem.