what does it mean
The usual meaning of "lexis" is the vocabulary of a language. So "characteristic lexis" = "typical vocabulary".
In literary criticism, "lexis" sometimes means the vocabulary and imagery of a particular author or text. But this is quite rare.
Halliday uses "lexis" in another sense, but it's very unlikely that that's the sense you require.
(If anyone else knows of any other ways in which the word is used, perhaps they'll post them later.)
All the best,