Well, I don't see much new here. Atzmon is correct that it shouldn't matter whether one believes or doesn't believe that the Holocaust happened to qualify one as being in solidarity with the Palestinians. But the real world doesn't work that way, and the plain fact that Palestinian solidarity is judged, in part, in the court of public opinion means that Holocaust deniers are going to be purged. It's too contagious a charge, like pedophilia.
The reason why it is, by the way, is that the vast majority of Holocaust denial is motivated by hatred of Jews.* Not a lot or a majority — a vast majority.** Indeed, Atzmon may be correct that Clark-Lowes is not an anti-Semite. It seems that many on the anti-Zionist left who espouse Holocaust denial do so not out of hate — or at least not purely out of hate. And, of course, some of them are Jewish (Hershkovitz, e.g.). I would argue that they are suffering from some kind of ideological cross-contamination with the far right in the case of anti-Semitism and are being led to believe denial theses because they're not seeing the whole picture.***
Indeed, I believe I could convince Mr. Clark-Lowes that he's wrong inside about ten minutes.
* As such, it reminds older generations of the Nazis, whom they personally fought. Thus, it's a non-starter for them.
** I think part of understanding how Holocaust denial and anti-Semitism are intrinsically linked has to do with understanding that if the vast majority of people in the world are convinced of a narrative that is fundamentally incorrect (in this case, that the Nazis conspired to kill the Jews of Europe, that they used gas chambers as one of the methods for doing this, and that they managed to kill in the neighborhood of six million), then the only thing that can explain this is a conspiracy to propagate this false point of view. Ultimately, the only party with a real dog in that fight would be "the Jews." See my essay here: http://holocaust-history.org/denial/abc-clio/
** I think an over-enthusiasm to rush to generalizations is probably the chief culprit.