It you want to get help and genuienly recover from suicidal ideation (or any mental health issue), being honest may be a better route, but there are consequences to it, unfortunately. Depending on the country you live in, it can become a lot harder to gain access to certain methods, you could fall into ridiculous amounts of medical debt, you could lose a lot of autonomy and freedom with everyday life, and you could be put on drugs for life that'll alter your neurochemistry; either for better or worse varying between each individual experience. I know I've been tempted to be honest about my situation in the past, but I always end up hiding it. I'd rather keep my options open than be further trapped/restricted in this life.