The proper line is "If you love these people so much, you can mourn for them!" but you got the gist of it.
Kal begs him to stop several times but Zod refuses and the final "NEVER!!!" is the breaking point for Kal, both literally and figuratively.
And as for Lois and Kal both, they had their memories probed during their time on Black Zero - we don't see it but when Kal saves Lois and they touch down in the wheat field she tells him that she's sorry but "they looked inside my mind" and he says pretty much the same thing happened to him. Perhaps with the DVD/Blu-ray release we might see that footage if that was filmed, with some funky Kryptonian mind-probe thingamabob or whatever.