Let me begin by saying I'm fairly new at this, and I'm not as experienced, etc.
When I first got my La Nouvelle Veine, I was excited to learn how to do Dilucot, but I was never able to really get it keen enough for shaving. I don't really have any long or thick hair to use for HHT, but I can usually get a fairly good idea with arm or leg hair. This was all a little frustrating to me, but I figured the only thing wrong was that I didn't have the experience. Switching to Unicot after a Dilucot seemed to work great practically every time. This always gave me a very smooth feeling, compared to other shave ready razors I had bought elsewhere. I don't know if doing the 100+ X strokes had anything to do with this, but I seem to recall reading someone doing that somewhere, and so I adopted it, but like I said, I never really got great results with Dilucot alone.
Next, I got a Les Latneuses. This was a whole lot easier for me to learn and use. I was able to reach a better keenness level a whole lot easier. I pretty much followed the Dilucot instructions by the book. With my particular hone and razors (mostly various Solingen's), I was getting what I thought were pretty good results.
Then, I wanted to go back to the La Nouvelle Veine, and see what I could do with it. I still have a little problem getting it as keen as it needs to be, so I often do a quick Dilucot on my Les Latneuses, and then switch over and do another Dilucot on the La Nouvelle Veine. It's probably overkill, but for me (my skill level, hones, razors, etc), it seems to work. Adding circles seems to help me (again, that's just me).
It seems like I get really good results if the edge coming off the Les Latneuses is really good (HHT-4 or so) and usable after stropping, or if the blade was pretty good to begin with and I skip the Les Latneuses. If I then go to the La Nouvelle Veine, I can keep that same HHT level. If the edge was poor to start with before I go to the La Nouvelle Veine, then I can't get it to improve all that much (again, that's just me). This is all with finishing on a very light slurry on the La Nouvelle Veine, rather than going to pure water. I do add a drop of water now and then when I do my 50 X strokes or so, but there's still a little slurry left.
I don't know if that helps, but at least for me, I can't make a huge improvement on a edge with my La Nouvelle Veine, and I don't know if doing a bunch of X strokes on plain water drops the HHT value, but think that might be the case.