No miralax isn't the same as lactulose. In the UK we call miralax movicol.

IMO Lactulose just doesn't cut it, I was put on that in the beginning, it did nothing for me, I was then put on Doc Sodium x3 a day which helped a little so I took them for 6 months then they stopped working and saw my DR who gave me Movicol and boy did I poop through the eye of a needle I stayed on that for a while but it irritated my fissure too much and set my IBS on meltdown, I then switched to Fybogel Mebeverine which I now blame for my current re-tear as my stools were too big

My CRS told me it was safe to take Miralax forever, if need be.