Which one is correct?
We introduce the xx model, which exploits the lack of consistency.
Or,
We introduce the xx model, which exploits lack of consistency.
If you ask me as a reader, both are grammatical and I just have to say that "(a) lack of consistency" stands for generality, and "the lack" for specificity" which is preferable in your sentence. But in the non-affirmative form "lack" is viewed as a mass noun such as:
"There was no lack of amusement at the theater."
Also, if you are using "lack" as a general reference [for its meaning], you could point out that if in singular, it really depends on your writing style, interpretation, or even approach.
