Are dental shots and locals for delivery everlife-threatening?

Yes: If given too much local anesthesia it can be life-threatening also, in an allergic case it can cause anaphylaxis which can lead to death. But generally they are among the safest anesthetics and the amount to overdose is way beyond what is typically needed.

Usually not: In children and patients with a heart condition or high blood pressure are at higher risk of "overdosing" with local anesthetics containing epinephrine. Epinephrine increases heart rate and blood pressure. It's extremely rare for a patient to die from too much local, but i suppose it is possible and more probable in that population.

Rarely: Under certain conditons, any injection can be life threatening. But in the vast majority, injections of dental anesthetic are very safe. Your dentist will know the appropriate dosages and techniques to keep you comfortable and safe. If you have other complex health issues, your dentist may confer with your md to make sure you are a good candiate.