Or, since (if I understand correctly) Substance Painter uses a transformed EXR file of a CMS pattern as a LUT, you could just run ctlrender on the linear_to_linear.exr file, applying the relevant CTL transforms.
Since the linear_to_linear.exr file covers only the 0-1 range, the resulting LUT will only cover input in that range. In order to correctly process values >1, you need to pre-transform the data before the LUT, and take account of this in your LUT baking. The Substance painter documentation says that the Tone Mapping function can be used to apply a lin to log transform, for example, although I don’t see any information on what the log function used is.
I must be clear that I am not specifically familiar with Substance Painter, so my advice here is from theory, not practical experience.
EDIT: Looking that the comparisons of UE4 and the LUT on the page you linked to, it would appear that their LUT does not use a pre-transform. The speculars look clipped in the Painter versions of the images, and properly rolled off in the UE4 ones.