Google yielded two answers. But Logan R. Kearsley, MA in Linguistics from BYU is too recondite. Can you please explain at the level of a 16 y.o.? What does "analytical level of a language that deals with vocabulary" mean?

A lexicon is a set or inventory of all the lexemes in a language. (What counts as a _lexeme_ is a whole other question all on it's own!)

Lexis is the _analytical level_ of a language that deals with vocabulary (as opposed to morphology or syntax). It's also defined as "the complete group of all words in a language", which, depending on how you define "word" vs. "lexeme", may or may not be the same thing as the lexicon. Languages with sufficiently productive morphology, for example, may have an infinite set of words (lexis), but will still have a finite _lexicon_ of lexemes that can be listed in a dictionary.

Vocabulary refers to a subset of words in a language that are used in a particular context or known to a particular person. Thus, you have "my vocabulary", "legal vocabulary", "vocabulary words for next week's quiz", and "the vocabulary you need to understand this book".

Siberia's comment is too brusque on detail.

Lexis usually refers to all words in a language that have a meaning but not their inflections.
Lexicon - this includes the morphemes.
Vocabulary - a list of words with an explanation.