Historians (of philosophy) often like to mock people who indulge in generalised ideas about past periods such as the Middle Ages. “You wouldn’t believe”, they will say, “how diverse they were. The idea that all their philosophy is in fact about God is quite mistaken.” But then they turn around, saying that the medievals were quite different from us, where “us” is indexing some unified idea of a current philosophical state of the art. What I find funny, then, is that historians will chide you for claiming something about the past that they are happy to claim about the present. Last time I checked there was no “current philosophical debate”.
Perhaps this is true of Martin Lenz's work in history of philosophy, but this is simply a distortion of history of philosophy in general. Some key points here:
(1) Martin Lenz is doing exactly what he is chiding historians of philosophy for chiding other people about: he is indulging in a generalized idea about the current philosophical state of things (in this case, what historians of philosophy are doing now). His entire argument depends on there being, in fact, a "current philosophical debate" in order for any of his comments about historians of philosophy to make sense.
(2) History of philosophy is, conceptually, evidential in method: it is concerned with evidence for what concepts, positions, and arguments actually have been. And when most historians of philosophy criticize something for anachronism, their criticism is chiefly an evidential one. You can't be anachronistic by merely being wrong, or giving an incorrect generalization; you are only being anachronistic to the extent that the evidence indicates that you have failed to account for some salient historical differences in your inferences about the past.
(3) In the case of "the Middle Ages", we have clear and definite reason to think that it is anachronism-risky, because we know how the category was formed: it is an artificial miscellaneous category. People did not develop it while looking at various philosophical positions and saying, "Hey, look, quite a few of these people in this place and time are exhibiting such-and-such patterns, or are responding to each other by such-and-such means." The very notion of 'middle' here means whatever is not on either side. Thus the classification conveys no information whatsoever about the kinds of historical differences that could matter to interpretation of philosophical concepts, positions, or arguments. It covers a thousand years with several different civilizations with different educational infrastructures, different means of communication, different cultural issues to deal with, and some of these have already been shown, by evidence to make a significant difference. It's not indulging in "generalised ideas" that is the problem: it is disregard for evidence and a lack of critical thinking about the concepts being used.
(4) I have never met anyone working in history of philosophy who did not use a cautious or qualified sense of 'us' or 'we' when contrasting past with present. There is nothing, for instance, in the Adamson rule that takes "we" and "us" to be unqualified. In fact, this is not a natural reading of the rule at all; the "we and "us" in question is given by the rule itself, and it is not universalized: "Instead of assuming that the historical figures we study are motivated by the same philosophical worries that worry us, we need to understand why they care about each issue they raise." What 'we' means here is 'we, who are studying them', not 'we, all the philosophers in the world right now'. What are Adamson's rules, in fact? Suggestions for best practice in studying philosophers historically. People doing this are the 'we'. In other contexts, the 'we' might be more narrow and indirect -- 'we, the people studying mind-body relations with reference to such-and-such theories', or what have you.
(5) This is shown in another way. Lenz is right that one thing that causes historians of philosophy to contrast past and present is that philosophers in the present sometimes want to know why the arguments are relevant. Most academic philosophers, in my experience, have a purely utilitarian conception of argument, for instance; they see arguments as things to be used. They don't have the love of arguments themselves, as beautiful things to be studied in their own right, that is necessary for serious history of philosophy. But they are our colleagues, and we have to explain ourselves to them, because that is what a great part of academic life is, explaining yourself to your colleagues. Thus this kind of contrast is quite often an attempt to bridge between one's own work and the work of specific colleagues, or else an indefinite but not very large group of them. This is not uncommon. Again, the 'we' is not unqualified.
(6) 'Synchronic anachronism' is an oxymoron; if he wants a label, a better one is needed. We are not 'anachronistic' beings except in the sense that we can move with the times; having a bunch of heritages traceable to different times is not what anachronism is. The fact that the heritages are there and are traceable is in itself evidence that they are relevant (in some way) to the time in which we are, which is precisely what you don't characterize as anachronistic, outside of maybe polemical contexts that are not particularly relevant to the ordinary practice of HoP. What Lenz is concerned with is ordinary hermeneutics, and doesn't depend on anything to do with times or anachronism.