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Success rate is affected by relative CP.
I don't know how Lullaby worked in the past, but over the past few days I noticed a definite success rate difference when swapping -CP gear around in shadow missions for skill training. I did some more formal tests versus groups of enemies (reducing my CP up to 2300 at a time) and I can tell you that right now, Lullaby's success rate is lowered versus enemies that are "stronger" than you.
3477 CP, R1 Lullaby against 3200/4200 enemies.
https://s31.postimg.org/mpu67ts3f/mabinogi_2016_06_26_002.jpg
1147 CP, R1 Lullaby against 3200/4200 enemies.
https://s31.postimg.org/ctt386mbf/mabinogi_2016_06_26_003.jpg
https://s31.postimg.org/lq3vc4cxn/mabinogi_2016_06_26_004.jpg
(And yes, of course this was repeated multiple times with the same results.)