preparing bathroom walls

Hi, we recently moved into a new council property and the local housing maintenance group came in and white washed all our walls except the bathroom. It seems they repaired all the holes in there but because the previous paint looks clean, probably left it as felt it looked suitable. My problem is that I cleaned the wall with sugar soap but am unsure whether to white wash it before painting or whether I can just paint. The current colour is light blue and we want to paint it lime green. What is the correct way of doing this. TIA

 

Well half the bathroom is covered in tiles so there's only a smallish area in which to paint but it's enough to make a difference