According to Derrida, deconstruction’s purpose is to expose the unconscious structure that governs any rigid form of discourse in order to make it fall through its own weight. No need to add anything to it.
This task could be achieved also through questioning.
By making questions that expose the underlying structure of any form of discourse in an atempt to undo the structure.
Lacan’s solution for this is the “Discourse of the Analyst”, a form of discourse that he borrowed from Aristotelian logic and serves the purpose to expose the nature of the “Master Discourse” , in other words, universal affirmative structures (generalizations, as you said) through particular negative lenses (discourse of the analyst).
For example, an obssesive neurotic patient may come with the next universal affirmative “All women are evil”, which has the form of the Master Discourse, one is taken as a slave by an universal affirmation that rules ones daily life and shapes ones experience.
A Lacanian analyst would use the “Analyst Discourse” by engaging in such universal affirmative with a particular negative: “Not all women are evil” and exposing to the patient how is it possible that not all women are evil through the patient’s own experience. Maybe by helping him to find examples in which women were not evil.
And therefore, allowing the patient to come to terms with his own castration, and accepting the uncomfortable unfounded and incomplete nature of his reality, rather than seeking safety on authorities and totalizations to make sense of his reality (TV news/religion/any form of Master Discourse)
IMO Lacan’s approach seems more effective than Derrida’s.
This happened because Derrida was a philosopher and Lacan had a bigger responsability in dealing with mental illness and issues of the mind.