Short answer: likely sometimes.
The gravitational potential of a galaxy is not going to be a spherically symmetric $1/r$ potential, since it is the sum of the potentials of all the stars, plus from a diffuse dark matter component. In particular it can be flattened.
That said, in practice one can decompose the potential using a multipole expansion where we in essence make a Taylor expansion in terms of powers of $1/r$. A flattened distribution will have a nonzero $1/r^2$ potential component, a more lumpy one quadrupole ($1/r^3$) and higher order moments. Since at large $r$ these terms vanish faster than the monopole $1/r$ term we well-separated, fairly spherical galaxies will in the large behave as mass-points. Hence there would be Lagrange points for the circular or elliptic restricted three body problem for them.
One can wonder if the corrections due to the multipole moments break the Lagrange points anyway. Without doing numerical simulations it is hard to tell, but a simple heuristic argument is that the L4 and L5 Lagrange points do exist for any $1/r^\alpha$ potential (I have still not found a neat way of showing this except reams of algebra). Hence extra multipole terms locally just perturb the potential as if it was not quite $1/r$, but there will be Lagrange points in the vicinity.
There is likely no hard criterion for the existence of Lagrange points in the general galaxy problem since even defining stability is subtle (real galactic mass distributions orbiting each other will change each other's shape, making the problem non-periodic). In the Local Group case Andromeda and the Milky Way are on their way to a multi-encounter merger that isn't possible in mass-point mechanics and would mean any Lagrange points would have to follow into the merger and then disappear. Plus M33 and other nearby galaxies are turning it into a n-body problem even if everything were just well-behaved mass points*.
[* In a n-body problem with chaos, generically there will be an infinity of unstable periodic orbits for the main bodies. Adding a test body to the resulting potential from one such periodic orbit generically also has an infinity of unstable orbits, so in a sense you can get "Lagrange trajectories" that return to the same place once a certain integer number of main body orbits have passed. However, I don't know if there is any guarantee that there is any trajectory that does this in one orbit, and I think it is super-unlikely (unless we choose the problem cleverly) that it would retain constant distance to two of the bodies.]