Difference between lexicon and dictionary

A lexicon is a list of words that belong to a particular language.

Sometimes, lexicon is used as another word for thesaurus (see below)

A dictionary is a list of words and phrases that are (or were) in common usage, together with their definitions - so a dictionary is different from a lexicon because a lexicon is a simple list and doesn't define the words.

A thesaurus is a dictionary of synonyms (different words and phrases that have the same or similar meaning).

Finally, for completeness, a vocabulary is a list of words that an individual knows or uses regularly. Vocabulary is different from lexicon because vocabulary is about what an individual or group of people know, whereas lexicon is about the language itself.

The accepted answer is not wrong, but it is incomplete.

If you look closely at the Wikipedia article on lexicon linked to in the well-upvoted comment on the question, you will notice an irony. Wikipedia says,

The lexicon (or wordstock) of a language is its vocabulary.

but has three footnotes to Liddell & Scott—that is, Henry George Liddell and Robert Scott's An Intermediate Greek-English Lexicon. In case you are not familiar with this tome, check out the link to λέγω given by the article. It's a dictionary, and a thorough one at that. In fact, it's something of a standard in the study of ancient Greek.

The same holds for a volume I recently bought—Gesenius's Hebrew-Chaldee Lexicon. He spends nearly three pages on the article, הַ—I'm talking three large pages with two columns and small font. You better believe that goes a beyond a regular definition—it's a rather thorough discussion of the grammar of the word.

The Free Dictionary provides the definition that covers this:

(Linguistics) a dictionary, esp one of an ancient language such as Greek or Hebrew

Indeed, from what I've seen, a very thorough type of dictionary indeed! In Biblical studies/ancient linguistics, a lexicon seems to be not less, but more, than a dictionary.