I can see why Poncirusguy advises painting the split, because it was long thought that painting the split was beneficial and gave some protection. However, research has shown covering with either tar or paint is not effective in healing bark splits. From the pictures you posted the splitting does not look to be caused by phytopthria. At this point if it was my tree I would watch it and presently do nothing. Bark splitting on lime trees is not all that rare. One last comment, did your lime tree go through a period of drought then a period of watering?