Should I lie to my therapist or will it be ok

I just started going to Pathways for postpartum depression and when I first got there they told me they had a private policy and they could share my information under certain circumstances but they didn’t elaborate. Does anyone know if they will tell the food stamp office who lives with me? They asked and I just told them me and my kids but I need to be able to be honest with my therapist. PLEASE NO JUDGMENT!! My situation is complicated and I cannot afford food for my family without them. We went 3 months without groceries before I broke down and told them my husband and I split.