As a linguist,l would consider a sememe the smallest unit of meaning. Very similar to a morpheme. For example, the -er in singer would be a sememe pointing to someone performing the action of singing. Sing- is another instance of a sememe in this sense.
Let me add an "afterthought" to my previous replies. This is made in order to clarify how "lexeme" and "sememe" interact/relate as concepts.
Yes, "faithful" is a lexeme consisting of the two sememes "faith-" and "-ful".
Hope this helps.