Answer:
The historical method.
Step-by-step explanation:
Lexicography is the process of compiling, editing, writing or making or dictionaries. There are over a millions of words in any language. In order to find out the meaning of each word and maintaining the originality requires extensive research.
While making or compiling a dictionary, a lexicographer needs to see the origin of the word, and what does that origin mean and how that meaning applies to the new formed word. To do this a lexicographer uses the historical method of research, since he will be looking back(past or history) to the origin of the word and the meaning of it.
In historical research method or historiography attempts are made to recapture the complexities of subtlety in a systematic manner.
So, it is the historical method of research used in lexicography.