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.
Best Answer
What is mandatory for contractors is suggested for homeowners.
Lead dust is what you want to avoid:
Common sense stuff: N95 (or better, EPA suggests N or P 100) dust masking, hand washing, clothing changing, sealing debris and plastic tarping in (appropriately tough, 3 mil ) plastic bags