The lexical syllabus is a form of the propositional paradigm that takes ‘word’ as the unit of analysis and content for syllabus design. Various vocabulary selection studies can be traced back to the 1920s and 1930s (West 1926; Ogden 1930; Faucet et al. 1936), and recent advances in techniques for the computer analysis of large databases of authentic text have helped to resuscitate this line of work.
The modern lexical syllabus is discussed in Sinclair & Renouf (1988), who state that the main benefit of a lexical syllabus is that it emphasises utility – the student learns that which is most valuable because it is most frequent. Related work on collocation is reported by Sinclair (1987) and Kennedy (1989), and the Collins COBUILD English Course (Willis & Willis 1988) is cited as an exemplary pedagogic implementation of the work, though “in fact, however, the COBUILD textbooks utilise one of the more complex hybrid syllabi in current ESL texts” (Long & Crookes 1993:23).
Sinclair & Renouf (1988:155) find that (as with other synthetic syllabi), claims made for the lexical syllabus are not supported by evidence, and the assertion that the lexical syllabus is “an independent syllabus, unrelated by any principles to any methodology” (Sinclair et al. 1988:155) is subject to the criticism levelled by Brumfit against notional functional syllabi, i.e. that it (in this case, deliberately) takes no cognisance of how a second language is learned. Since these observations were made, however, Willis (1990) and Lewis (1993) have gone some way to provide such a theoretical justification.
You can find more about it in this article from the Cambridge University Press