Drain the tuna and set it aside. Drain and rinse the cannellini beans under cold water until the liquid runs clear.
Slice the red onion thin and put it in a large mixing bowl (4-quart / 3.8 L) with 1 tbsp of the lemon juice. Let it sit for 5 minutes, this softens the sharp bite.
Halve the cherry tomatoes, dice the cucumber, and add both to the bowl with the onion.
Add the drained beans, olives, capers, and parsley to the bowl.
Break the tuna into large chunks with a fork and add it on top.
In a small bowl, whisk together the olive oil, remaining 1 tbsp lemon juice, red wine vinegar, grated garlic, salt, and pepper.
Pour the dressing over the salad and toss gently so the tuna stays in chunks instead of breaking apart.
Taste and adjust the salt, remembering the olives and capers are already salty.
Serve right away, or chill for 20 minutes so the flavors have time to blend.