In large serving bowl, mix together blackeye peas, chick peas, kidney beans, cucumbers, peppers, and cilantro.
In small bowl, whisk together vinegar, salad and vegetable seasoning, and lemon juice. Slowly drizzle in olive oil, whisking constantly, until blended. Pour dressing over bean mixture. Toss well to coat completely.
To help the flavor of the dressing make its way inside the bean (instead of just flavoring the surface), heat the dressing until warm before mixing with the beans (a 1 minute zap in the microwave will do the trick). Then, mix and refrigerate until cold.