Thanks, Dave. I think I requested the Biometrika and I'll look into the 2nd one when I get back to home base next week.
Yes, I see why checking delta F(x) and delta F(x-) at each sample datum x solves the problem. I wonder though whether the Lilliefors thresholds (for example, in their paper) were generated with the statistic defined in this way. Or is it the case that nowadays there are a plethora of threshold tables, each with their own particular definition, ideally documented to this level of detail.