Drizzle- it really, really isn't. You're now changing the first /æ/ sound into a schwa?
The "problem" with the Italian /e/ vowel sound, like the Italian /I/ vowel, is that the British English /e/ is slightly shorter than the Italian one, acoustically. So we tend to turn it into an "ay" . The reality is that the Italian pronunciation of the sound is some way between the short "e" of "bed" and the long "ay" of "play".
It's the same with the "i" which is why Italian learners of English have more trouble with words like "ship" and "sheep" than with other, arguably more complex sounds.
The "a" at the beginning isn't as problematic. Italian /a/ is very slightly longer but not that it makes a difference. It's the British pronunciation of the Italian word that's turned it into /la:tei/ with the longer /a:/ at the beginning.
Yappety- "draw" is a perfectly acceptable standard variation of the pronunciation, though if you listen very carefully, and in isolation, you'll hear that many of the speakers we think are saying "draw" are actually saying "drawer" but with a very very weakened schwa for the second syllable.
As language evolves (to the delight and fascination of the true linguist) (David Crystal: "if it is said, it is correct") I imagine the spelling of drawer will also be modified.
Not sure we'll be allowed to apply adverbs to nouns quite yet though 