gravity - Tide on the Moon

The tide would be locked in place, roughly, because the Moon always shows the same side to the Earth (tidally locked). But the height of the water at the location facing the Earth and the opposite side should be greater than the mean height, and at the limb, as we see it, the height will be lower than the mean but by half the magnitude of the high tide.

Imagine installing a pipe with cross-section 1 cm$^2$ from the top of the ocean at its high point down to the center of the moon and then back up to the top of the ocean at a point where the net tidal field from the Earth is 0. Fill it with water until one side is equal with the water level on one side and its level on the other side will automatically be equal to the water level there. The weights of the water on both sides need to be equal if it is static. For now, we will ignore that g changes when one gets deep into the moon. Therefore, roughly speaking $rho$gh should be the same in both sections of the pipe, and:
$$
rho(g_M - g_t)(h_t + r_M) = rho g_M r_M
$$

where $g_t$ is tidal acceleration
$$
g_t(Moon) = 2frac{GM_Er_M}{d^3}.
$$
Subscript M means Moon and E means Earth and d is the separation between the Earth and Moon. Solving for h$_t$ gives:
$$
h_t = frac{g_tr_M}{g_M - g_t} sim frac{g_t}{g_M}r_M
$$
We could substitute values in here, but if we do this in comparison with the height of the tide on the Earth, 54 cm, we cancel out some of the error in the approximation and get an even simpler formula, namely,
$$
frac{h_t(Moon)}{h_t(Earth)} = frac{M_E}{M_M} frac{g_E}{g_M} Big(frac{r_M}{r_E}Big)^2
$$
The mass of the Earth is 81.3 time greater, the acceleration at the surface of the Moon is 1/6.25 of Earth's g force, and the diameter of the Moon is 0.2725 of the Earth. So, that is 81.3*6.25*.2725$^2$ = 37.7 time higher than the Earth's tide or 37.7*54 cm = 20.4 meters. Note that the height of the ocean does not matter as long as it is considerably more than 20 meters.

On the other hand, the water would begin boiling since it is at 0 pressure until a water atmosphere is created, but the moon is too small to hold an atmosphere for long and the whole ocean would be gone in a while.