Lime juice and baking soda is a combination to whiten teeth. It is very effective, and it is actually a “secret” revealed by one dentist. Fresh lime juice on baking soda produces a lot of foam. The foam is oxygen that is released. The chemical reaction is a simple combination of an acid (lime juice) and a base (baking soda). This elementary chemical reaction produces an excess of oxygen. The same chemical reaction results when vinegar and baking soda are combined. This vinegar and baking soda combination also whitens teeth very effectively.
The cleansing property of oxygen is also the basis for commercial products like Oxyclean.
Lime juice is edible. Baking soda, well, one prefers not to ingest it. However, using a toothbrush to pick up some baking soda and to brush the teeth with vinegar in the mouth is absolutely harmless.
A rather ignorant Chinese doctor once recommended using salt to brush the teeth. This is very bad, repeat, very bad. Salt damages the enamel of the teeth, and it can make the teeth brittle.
Never use salt as toothpaste. Use lime juice and baking soda or vinegar and baking soda as toothpaste. I was told by several people including one of my students that some Hollywood celebrities use lime and baking soda to whiten their teeth.