"I do not know any lawyers."

Translation: Nie znam żadnych prawników.

[IanIanIanIan_]

so Most of the time not knowing X results in genitive case?

[immery]

not doing anything usually results in genitive case.

negation means direct object changes from accusative to genitive.

[Juanjo159693]

Yes, all negative sentences use genitive (dopełniacz)

[Okcydent]

Not all, only accusative changes to genitive. The rest of cases stay as they were.