How can I mount a mailbox on a stucco wall?
10-15 pounds seem heavy for a mailbox but even plastic drywall anchors are rated higher than that for so I don't think the weight is going to be a problem.

That's a drywall anchor.  A lead anchor look similar and is typically used on brick siding but depending on depth of stucco it is possibly you could rely on a lead anchor in stucco.

What you really want is to mount the mail box through the stucco to the sheathing that is behind the stucco.  Depending on your wall assembly details - year of construction / climate - the sheathing can be 1/2" away from the surface of your stucco or 1 3/4"+ away or anything in between.  

The sheathing is going to be wood so really all you need is to pilot through the stucco until you reach the wood.  You should choose some corrosion resistant fasteners - deck screws #8 would likely be good.  Opt for 1/2" + thickness of wall before shealthing plus depth required to mount mail box (if metal 1/8" is probably fine).  If you've already drilled through the stucco then you can probably note at what depth the wood starts as the drill will behave differently as it goes through different material.  If you were using a hammer drill with a masonary bit that bit will likely stop when you hit wood.  This assumes a concrete type stucco and not an acrylic stucco which I haven't dealt with before.

It wouldn't hurt to fill the hole with caulking before mounting the mailbox to the stucco to prevent any water ingress.

Good luck.