Blanch green beans in boiling salted water 2-3 min, until tender/crisp, then shock in ice water to chill. Drain.
Zest lemons, then juice one and section the other. Melt butter in a large sauté pan. Add to the pan: anchovies, shallot, garlic, salt and pepper, then sauté 2-3 min, stirring to break down the anchovy. Add lemon juice and half the zest and green beans, then toss to coat and warm through. Add the butter beans and diced lemon sections and toss once or twice to warm and mix (the butter beans are delicate and will break down a little).
Taste and adjust salt and pepper, as needed. Transfer beans to a platter and garnish with reserved lemon zest, mint and a drizzle of olive oil.