The Diversity Immigrant Visa program, also known as the green card lottery, is a United States congressionally mandated lottery program for receiving a United States Permanent Resident Card. The Immigration Act of 1990 established the current and permanent Diversity Visa (DV) program.
Nepal is eligible for the Diversity So, you can apply if you pass the requirement.
Nations which are ineligible for EDV 2019 are Bangladesh, Brazil, Canada, China, Colombia, Dominican Republic, El Salvador, Haiti, India, Jamaica, Mexico, Nigeria, Pakistan, Peru, Philippines, South Korea, United Kingdom (except Northern Ireland) and Vietnam.
If your country is not in the list then it means your country is eligible.
Note: This is from an unofficial source, the official is not yet available.