To be eligible to serve as President of the United States, an individual must meet the following qualifications according to the U.S. Constitution:
- Be at least 35 years old.
- Be a natural-born citizen of the United States.
- Have been a resident of the United States for at least 14 years.
Now, let's analyze the individuals listed in your question:
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A 45-year-old naturalized citizen who has lived in the U.S. for 30 years: Not eligible due to being a naturalized citizen instead of a natural-born citizen.
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A 35-year-old born in the U.S. who has lived in the country for 14 years: Eligible as they meet all three criteria.
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A 36-year-old born abroad to U.S. citizen parents who has lived in the U.S. for 14 years: Eligible as they qualify as a natural-born citizen due to being born to U.S. citizen parents.
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A 40-year-old born in the U.S. who has lived in the country for 20 years: Eligible as they meet all qualifications.
Based on this analysis, the individual who would NOT be eligible to serve as President of the United States is the first option: A 45-year-old naturalized citizen who has lived in the U.S. for 30 years.