Bring a large pot of water to a boil. Add 1 tablespoon of salt. Cook baby potatoes for 12-15 minutes (depending on size). Use a fork to test for doneness. Drain, peel, and cut in half.
Trim green beans. Fill a 4-quart pot with water and bring to a boil. Meanwhile, prepare a bowl of ice water. Cook the green beans in boiling water for 30 second. Use a slotted spoon and transfer the cooked green beans into the bowl of ice water. Chill for 2 minutes. Remove, pat dry, and cut green beans into thirds.
Chop bell peppers and red onion. Mince garlic and finely chop dill.
Making The Lemon- Dill Dressing
Whisk olive oil, lemon juice, lemon zest, and sugar until the sugar dissolves. Add mustard, minced garlic, and chopped dill and whisk until well combined.
Making The Green Bean and Potato Salad
In a large bowl combine potatoes, green beans, red and yellow bell peppers, and red onion. Pour dill lemon dressing over the vegetables and combine well. Cover the bowl and chill in the fridge for 30 minutes. Remove and season to taste with salt.