First person narrative is just a device, and it doesn't necessarily imply that the narrator lives through the story. For example, plenty of horror stories end with something on the lines of:
And then the beast's bloated tentacles began to squeeze me. The world grew dark, and I knew no more.
...or some such. (Shel Silverstein did this in True Story, although that's tongue-in-cheek...)
The point is, first-person doesn't mean the narrator actually sat down after the story ended and wrote a book about it. It's just a choice of style and narration.
I will grant that some readers will expect (incorrectly) that first person means the character lives, but if this were a serious barrier, you could have no first-person fiction relying on suspense from danger to the narrator's life. (Suicide isn't your problem here; it's "did the character make it to the end of the book or not.")
Your best guideline is to write the story as you see fit, and then get some reader reactions to it. If people tell you "Listen, this didn't work because I knew the character lives," then fine, figure out a way to change it. If they don't then you're fine.
The one exception to this is: if you first person narrator is actively referring to things that happen "later." For example, How I Met Your Mother is essentially in past-tense/first-person, but the narrator is established as "telling the story to his kids." He drops references like "That's how I met your Aunt Robin" or "Of course, we only found out about that years later" - which clearly establish a lot of facts about what happens after the primary story is over. If you do that, then yes, suspense over "Will the narrator live through the story?" will be very weak (similar to how in How I Met Your Mother, suspense over "Will this relationship be Ted's Happily-Ever-After?" was very weak and usually not the focus).