Yesterday I discussed satellite photography. As I mentioned, there are problems with this technique, but there are others that might do the job just as well.
Consider a very simplified radar: you send out a pulse of radio waves, and you wait for reflections to come back. The longer the reflection takes, the farther away the thing that's reflecting.
During the Cold War, the US satellite reconnaisance researchers developed radar into a way to find concealed underground missile silos, and then as a demonstration published images of the network of underground rivers beneath the Nile delta, if I remember correctly. This worked by getting reflections back off features progressively deeper into the ground.
So this could work for looking for lava tubes. Mount a big radar on a Moon-orbiting satellite, and then set it looking at the surface of the Moon. Most of the time it'll get one reflection back, from the surface, but when it encounters a lava tube it'll get another reflection back from the tube roof, and then a third from the tube floor. This proposed mission would in fact provide two useful sets of data: a three-dimensional map of the Moons surface, which could be useful in mission-planning or geological studies, and then lava tube positions as a by-product.
There are naturally a couple of problems to overcome with this technique: on a basic level, resolution, penetration, and signal to noise ratio . Resolution is very important, as to find the sorts of lava tubes we're interested in we need a 10 m resolution, or even finer. Penetration is also important, as we want to find lava tubes even quite deep down, and a low signal to noise ration is vital if we want to extract any useful data at all! To get a high resolution, you need a high frequency, but increasing the frequency of the radar signal reduced the penetrating power. It's a thorny issue. Additionally, to get a 10 m resolution you'd need to know the position of the spacecraft to within 10 m.
Even with those problems, this seems to me to be the most economical way of getting the sort of data that would be useful for finding the sort of lava tubes suitable for locating a Moon base in.
So what are the last two methods?
 T.L. Billings, 'Re: lunar resources/lava tubes', sci.space.tech, 25-01-1996