This isn't exactly my "area of expertise", but here are a few ideas:

Draw the lines on PGraphics, then blend the PGraphics
Add an alpha channel
Create your own blending function

It seems that it works with different PGraphics, thanks, but I'm not able to make the line strokes have round corners.
I'm trying to do:

1. PGraphics PG;
2. ...
3. PG.strokeJoin(ROUND);

While I had before, simply,

1. strokeJoin(ROUND)

before my beginShape()
any clues?

Try with a Java2D PG, perhaps (just guessing).

Thanks this definitley works, the only drawback in using PGraphics and blend() is that I cannot record to PDF