Lasersohn as a Truth Relativist, MacFarlane style

I remember there was a discussion at some point between Dan LdS and Manolo CG about whether Lasersohn is a "non-indexical contextualist" or a "relativist" (MacFarlane's terms). The discussion concerned Lasersohn's 2005 paper, "Context dependence, disagreement and predicates of personal taste", where, with the exception of a short paragraph whose interpretation sparked the debate, there is nothing to base a relativist interpretation on ("relativist" - mind you - as opposed to "non-indexical contextualist"; there's no question whether Lasersohn is a contextualist of the ordinary sort.) However, in his more recent paper, which we were supposed to read in our unofficial reading group on contextualism and relativism last year, things are crystal clear. Here is what Lasersohn says in "Quantification and perspective in relativist semantics", Philosophical Perspectives 2008:

What makes this system “relativist”? Different authors use this term in
different ways. As I understand it, there are two crucial features of the system
just outlined which make this term appropriate. First, sentences may vary in
truth value without a corresponding variation in content. Second, this variation
depends on some parameter whose value is not fixed by the situation in which a
sentence is used. (pg. 315)
And then he continues, relating his view with MacFarlane's:
These criteria are equivalent, as far as I can tell, to the claim that sentences
may be assigned contents whose truth values depend not just on the “context
of use” but also on the “context of assessment” (MacFarlane 2003, 2005a). We
treat the context of use as fully determined by the situation in which the sentence
is used; if truth values vary independently of this situation, we regard them as
at least partly dependent on a separate context determined by the situation in
which the sentence is assessed for truth or falsity.

Maybe the debate was solved months ago, but I thought I should mention it anyway!