  We prove a Thomas--Yau-type conjecture for monotone Lagrangian tori
satisfying a symmetry condition in the complex projective plane
$\mathbb{CP}^2$. We show that such tori exist for all time under Lagrangian
mean curvature flow with surgery, undergoing at most a finite number of
surgeries before flowing to a minimal Clifford torus in infinite time.
Furthermore, we show that we can construct a torus with any finite number of
surgeries before convergence. Along the way, we prove many interesting
subsidiary results and develop methods which should be useful in studying
Lagrangian mean curvature flow in non-Calabi--Yau manifolds, even in
non-symmetric cases.
