Heat a good amount of salted water to boiling in a large pot. Add the green beans and return to a boil. Cook 2-3 minutes until they are just barely tender crisp. Remove with slotted spoon and place in an ice water bath.
Add the potatoes into the same pot and cook until tender 10 -12 minutes. Drain and rinse under cold water. Spread them out on a dish towel to dry and cool slightly.
Cut the potatoes in half and put them in a large mixing bowl. Add the green beans to the bowl along with the onions.
In a jar combine the olive oil, vinegars, mustard, garlic, and lemon juice. cover tightly and shake until well blended.
Pour the dressing over the vegetables and toss to coat everything. Taste and add salt and pepper if needed. Cover and refrigerate for several hours to let the flavors blend.
Remove salad from refrigerator an hour or so before serving. The flavor is best at almost room temperature.