In a small bowl, whisk together the olive oil, red wine vinegar, Dijon mustard, salt, and pepper to create the dressing.
Divide the dressing evenly among four 32-ounce wide-mouth mason jars (approximately 2 tablespoons per jar).
Add the cooked potatoes and blanched green beans as the first layer to allow them to marinate in the dressing without wilting.
Add a layer of cherry tomatoes, Kalamata olives, and capers to each jar.
Distribute the flaked tuna evenly across the jars, followed by the quartered hard-boiled eggs.
Fill the remaining space in the jars with the torn Bibb lettuce, ensuring the greens do not touch the dressing at the bottom.
Seal the jars with airtight lids and refrigerate for up to 4 days.
To serve, shake the jar vigorously to distribute the dressing or invert into a large bowl.