I applaud you for covering Althusser for a general audience! I am a PhD candidate in critical theory, so I appreciate seeing Althusser mentioned here on Medium. That said, when it comes to Lacan, ideology is part of what he calls the symbolic order. This is the realm of language, and ultimately, the unconscious. Althusser’s major intervention with regard to ideology is to say that it essentially functions at the level of the unconscious, that it operates at a level that comes before us, that it interpellates us into our position in society as though we were objects rather than subjects. As per Lacan, our subjectivity, our sense of self, is part of the imaginary order, and thus, Althusser builds on this (and on Marx and Engels in the German Ideology, as you astutely pointed out) in his critique of ideology to say that ideology is an apparatus of state used to reproduce the capitalist mode of production rather than something that a person can claim as his or her own. Zizek, of course, has lots ot say about this in his magnum opus The Sublime Object of Ideology, in which he builds on both Lacan and Althusser.