It’s not clear from your description what happened - you said completed but failed? Which was it? they require
successful completion of high school. Her vocational studies will not help her for DV.
The complete description of what successful completion of high school means is here (this is the manual the CO uses to adjudicate)
High School Education or Equivalent:
(1) (U) You must adjudicate the DV applicant’s qualifications under this requirement. In order to enter the DV lottery or apply for a visa under the DV program, the alien need not prove that this requirement is met. The DV applicant must, however, meet this requirement by the end of the fiscal year in which selected and present evidence of completion to the satisfaction of the consular officer. If the applicant does not meet the requirement at the time of the visa interview, then the applicant is not eligible as a diversity immigrant under INA 203(c)(2) and the proper basis for refusing the case is under INA 203(c). If the applicant presents evidence of completion of high school before the end of the fiscal year, and visas are still available for the region, you may overcome the refusal.
(2) (U) “At Least a High School Education or its Equivalent” Means Successful Completion of at least a:
(a) (U) Twelve-year course of elementary and secondary study in the United States; or
(b) (U) Formal course of elementary and secondary education comparable to completion of 12 years of elementary and secondary education in the United States. Because a United States high school education is sufficient in itself to qualify a student to apply for college admission, in order for a foreign education to be equivalent to a United States education, it should be sufficient to allow a student to apply for college admission without further education. Vocational degrees that are not considered a basis for further academic study will not be considered equivalent to United States high school education.
(3) (U) Education Requirements: “At least a high school education or its equivalent” in this context applies only to formal courses of study. Equivalency certificates (such as the G.E.D.) are not acceptable. To qualify, an alien must have completed a 12-year course of elementary and secondary education in the United States or a comparable course of study in another country. Evidence might consist of a certificate of completion equivalent to a United States diploma, school transcripts, or other evidence issued by the person or organization responsible for maintaining such records, which specify the completed course of study.
(4) (U) Education Evaluation:
(U)
The burden of proving that an applicant's education is equivalent to a high school degree is entirely on the applicant. If the applicant does not satisfy you that the applicant's education is equivalent to a high school degree but you believe additional evidence could meet the applicant's burden, the appropriate basis for refusal is INA 221(g). You may request the applicant to provide additional information. If the applicant is unable to credibly prove the education equivalency requirement to your satisfaction, the appropriate basis for refusal is INA 203(c).