Look me is used in certain expressions in English.
Look me in the eye and tell me that!
One year they interviewed the girl scout who had sold the most boxes of girl scout cookies. She had sold an incredible number of boxes. When they asked her what the secret of her success was, she replied:
You need to look people straight in the eye and make them feel guilty.
“Look me”, is incorrect. “Look at me”, on the other hand, is correct English. It is a request (from the speaker) for attention; to see (speaker’s) body/figure or move the eyes towards (that person). “Look at” is a phrasal verb, which is a combination of a verb (“look”), with a; preposition (“at”), but could also have the combination; verb + preposition +/- adverb.
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