The published clinical trial shows most patients (76%) responded by 4 weeks to LDN, but some took 8 weeks to respond. (Of course, like any med, it didn't work for every patient.) So it looks like you need to give it at least 4 weeks, and up to 8 weeks, to achieve a response. If by 8 weeks there is no response, then the likelihood of achieving a response is slim-to-none.
Of course, response doesn't mean remission. By one month 29% achieved remission, and by two months it was 53%. "Remission" in the clinical trial was defined as a CDAI score of 150 points or less.
The clinical trial says CRP decreased from a median value of 2.6 (it says "normal" is less than .8) at baseline to a value of .9 by the 12th week. ESR (sed rate) also decreased.
The trial had only 17 participants, and followed them for only 16 weeks, so there is no long term clinical trial data on LDN.