"But, given his very narrow underlying assumptions, it seems plausible to doubt the robustness of Lucas’s conclusion. Proving the validity of a proposition requires more than constructing an example in which the proposition is shown to be valid. That would be like trying to prove that the sides of every triangle are equal in length by constructing a triangle whose angles are all equal to 60 degrees, and then claiming that, because the sides of that triangle are equal in length, the sides of all triangles are equal in length."One of the things Glasner suggests is making the demand of firms correlated with each other, rather than independent as Lucas presents it. One paper that does this that comes to mind is Akerlof, Dickens, and Perry (2000), and Glasner's intuition is right - they do get an exploitable Phillips Curve. Granted, it's the "near rational behavior" and not the monopolistic competition that gets them that.
This is all interesting as an alternative to Lucas's Phillips Curve, but I never really thought of that as the point of this paper. The point, I thought, was simply to demonstrate that observed aggregate relationships aren't necessarily exploitable by policymakers: you need to do more work if you want to demonstrate exploitability.
To use Glasner's analogy, the way I read Lucas's argument is that he came across people who were saying or strongly implying that there were no triangles where all sides were of equal length and Lucas presented one exception to demonstrate that such a thing could not be assumed.
What's interesting is that although I don't think anyone believes Lucas's actual Phillips Curve model, these "Lucas supply curves" are used in models because they're a nice way of incorporating the basic logic of the signal extraction problem facing firms as well as inflation expectations. So even in cases where demand may be monopolistically competitive you're still liable to see a Lucas supply curve hanging around.