On the half-plane, we prove Lyapunov stability of finite sums of Lamb dipoles under the initial assumptions that they are sufficiently separated and that the faster dipoles are positioned to the right of the slower ones. Our approach combines sharp energy estimates near the Lamb dipoles with a Lagrangian bootstrapping scheme, enabling us to quantify the exchanges of circulation, enstrophy, impulse, and energy between various parts of the solution. We shall discuss several extensions of the result, which shows flexibility of the method. This is joint work with Ken Abe (OMU) and Yao Yao (NUS).