Torsion anomalous points and families of elliptic curves

We prove that there are at most finitely many complex $\lambda \neq 0,1$ such that two points on the Legendre elliptic curve $Y^2 = X(X-1)(X-\lambda)$ with coordinates $X = 2,3$ both have finite order. This is a very special case of some conjectures on unlikely intersections in semiabelian schemes.