The meaning of "view as"

Yes, you can add which or that after "lawmakers" (I would personally add whom in this context). The relative pronoun whom (or which or that) is not missing, it has just been elided.

Other companies are focusing on lawmakers (whom/which/that) they view as complicit in Trump's effort to disrupt the affirmation of Biden's election win.

So the sentence is correct with or without it, just as when we say The people I know instead of The people whom/that I know.

As for "view as", the phrase means (WordHippo):

• To regard or view in a given way
• To regard or consider in a specified way
• To refer to or consider (someone or something) as being

It can be followed by a noun (phrase) or an adjective:

Life on the set is pervaded by what the uninvolved might well view as (or consider) superstition. ("view as" + noun)

Cronin and Magdalinski want an alternative to the current political process, which they view as unrepresentative of real-world needs. ("view as" + adjective)

In the last sentence I have underlined which, because it relates to your first question about whether you can put in a relative pronoun or not.