How small of an opening should a lintel be put in?

It's not a question of opening size but a question of loading over the opening. No load, no lintel. If a 12 inch opening is capped with a 16" block, the block is the lintel. If an opening is between wall studs there is little need for anything that would be called a lintel. Anouther name for a lintel is a header. There is usually some kind of header over an opening. A lintel's size and integrity is determined by the load it will support.