Here's a similar type of stucco to what I have:
Mine is light yellow but similarly rough-seas wavy like this picture. Mine is also now looking pretty dingy and I would like to repaint. Upon closer inspection I found that the paint on there now is flaking off in thin, holey flakes. I read that this is a good indicator of lead-based paint; my house was built in 1925 so this would not surprise me in the least.
I started calling around to abatement places but got the runaround. I feel like I could do this myself. But I'm not usually very careful about keeping a surgically clean work area or cleaning up super perfectly, and if this is something that is required with lead paint then I might be better off paying somebody to do it for me.
But if not ... how would I go about doing it? Chemical or UV lamp? How would I need to set up drop cloths to catch the flaky bits that fall off? How to I need to dispose of it? Would welcome detailed instructions from anybody with experience.