I think it's hard to say whether your odds get better in second grade. Vacancies occur in the later years because of seats added and also attrition. In first grade, they always add 1 seat per class plus there's a reasonable chance that someone finished the kindergarten year and decided it wasn't for them. I believe kids are also still getting counseled out during first grade (they move the waitlist during the first half of the year). In second grade, they add 0 seats, and after 2 years in the program, I think kids are more committed (unless they move). So maybe 100 people enter the lottery in first grade and 15 people enter in second grade. If there are 4 seats for first grade and 0 seats for second grade, your odds are still better for first.
That said, they do add seats to the program in the later years and they do rely on native speakers to fill those spots. I think the challenge is that if you are trying to maintain a language at home, I have heard the tests they have to pass are not easy. They want them to have grade level reading, writing, and speaking proficiency.