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Lexicography is either of two things
A person devoted to lexicography is called a lexicographer.
General lexicography focuses on the design, compilation, use and evaluation of general dictionaries, i.e. dictionaries that provide a description of the language in general use. Such a dictionary is usually called a general dictionary or LGP dictionary. Specialized lexicography focuses on the design, compilation, use and evaluation of specialized dictionaries, i.e. dictionaries that are devoted to a (relatively restricted) set of linguistic and factual elements of one or more specialist subject fields, e.g legal lexicography. Such a dictionary is usually called a specialized dictionary or LSP dictionary.
There seems to be a discussion of the definition of lexicology. Some use that word as a synonym for theoretical lexicography, others use it for a branch of linguistics pertaining to the treasure of words in a particular language. It is now widely accepted that lexicography is a scholarly discipline in its own right and not a sub-branch of linguistics.
Most English lexicographers would find interest in Samuel Johnson's Dictionary of the English Language (1755). He famously defined a lexicographer as "A writer of dictionaries; a harmless drudge that busies himself in tracing the original, and detailing the signification of words".
Introductory books to lexicography:
See also: Monolingual learner's dictionary