Can having very low iron levels kill you?

Not strictly: Low iron levels produce anemia. Anemia when severe can kill, but that occurs very rarely since symptoms usually bring you to the doctor early. Body is very good at maintaining iron levels. It is typical for menstruating and pregnant females to have mild iron deficiency and sometimes anemia. This is usually treated with a little iron replacement or meds to reduce menstrual loss.

Can cause anemia: Low iron levels lead to anemia, which depending on how severe can make you feel weak, tired and if severe bleeding occurs, it can lead to death.

Theoretically, yes: You'd have to have REEEEAAAALLLLLY low iron levels to do this, but REEEEAAAALLLLY severe anemia of very long standing could conceivably put you into high-output cardiac failure which if prolonged over a few years could cause cardiac arrest.