preposition
A word that shows the relationship between a noun (or pronoun) and other words in a sentence. In this case, 'on' indicates the position or location of being 'the lookout for'.
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The security team is constantly on the lookout for any suspicious activity.
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I'm always on the lookout for good deals at the grocery store.
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The detectives are on the lookout for the perp in the neighborhood.
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She's always on the lookout for new opportunities to grow her business.