The charge of "psychologism" - which Frege made against Husserl, Shpet's teacher, for example - was that someone was reducing logic to psychology; turning the timeless and universal laws of reason into merely the way people happen to think, with all the imperfections that this involves. The counter charge would have been "logicism," that someone is treating as necessary and analytic matters that are in fact contingent and synthetic.
So LSV was willing to risk the accusation of psychologism; he rejected the notion that the inner form of the word is a timeless, universal essence, and instead located it in history. He was not separating word meaning entirely from sense, though he did, however, argue that word meaning is the most stable aspect of sense.
And the issue that would then have confronted him is whether he could build a convincing account of the genesis of reason using changing and contingent building blocks. Could he build logic from psychology? Or was he willing to propose a psychological account of logic? He does, seemingly approvingly, quote Lenin on the notion that logical truths are simply the result of millions of years of repetition of habits. I must say that I find that rather unsatisfying.
Martin