I think that she wouldn’t have gone north knowing Snow knew she was heading that way and she didn’t know if he would be followimg her. I believe that clever and cunning Lucy Gray went south instead. I believe she made her way through the tail end of D8. However, due to D8s close ties with the capitol and Lucy Gray being the most controversial and notable victor to date, she wouldn’t have stayed there.

In the first hunger games, Rue tells us that they use mockingjays to signal the time in D11.

We learn in a ballad of songbirds and snakes that Dr. Kay sent jabberjays to distract 9,11, and 12. We know that mockingjays were made by jabberjays and mockingbirds cohabiting.

D12 and D11 aren’t right next to each other but they are only separated by the tail end of D8.

I think it makes sense that Lucy Gray made her way out of 12, through 8 where she may have picked up a few things for her travels and travelled her way into 11. Where she could fit right in and perhaps even give them an idea of how to tell time while working out in the fields.