In a large bowl, combine the rinsed and drained great northern beans and cannellini beans. Drizzle with the olive oil, 1 tablespoon of fresh lemon juice, and 1/4 teaspoon salt. Gently toss everything together to coat the beans evenly. Set the bowl aside to allow the flavors to start melding.
While the beans are resting, prepare the dressing. In a small bowl, whisk together the dill pickle juice, 1/2 tablespoon lemon juice, red wine vinegar, minced garlic, 1/4 teaspoon sea salt, and ground black pepper until the mixture is well combined and emulsified. I like to use freshly squeezed lemon juice for a brighter, more vibrant flavor.
To the bowl with the tossed beans (from Step 1), add the thinly sliced red onion, halved cherry tomatoes, sliced dill pickles, and chopped fresh dill. Toss the mixture gently to evenly distribute the vegetables and herbs among the beans.
Pour the prepared pickle-dill dressing (from Step 2) over the bean and vegetable mixture (from Step 3). Gently toss until everything is thoroughly coated and combined. Taste and adjust seasoning with more salt if needed. The salad can be served immediately for a fresh taste, or you can refrigerate it to let the flavors meld even more.