I recently had 6 sessions of iLipo, I also had tubal ligation 5 years ago.. Does iLipo melt the tubal ligation?

The liposuction cannula should go nowhere near the fallopian tubes. There is no chance that The repair would be damaged by liposuction.

iLipo should not have any effects below your abdominal wall. So the tubal ligation would not be affected. 

No, the effects of iLipo are confined to the area between the skin and the muscle layer of the abdomen wall. Your fallopian tubes are within the abdominal cavity below the muscle layer the abdomen and will not be affected.