I'm using LIS3DH accelerometer, a 3 axes accelerometer to build a low energy consumption device. For now I just need the Y axis. If I disable X and Z, can I save more energy or the accelerometer use the same amount of power?
You can disable individual axes on that part with CTRL_REG1. It doesn't say that this saves power.
There's quite a lot of power-saving tips in that document, including a claimed consumption of 2uA. Probably the best thing is to put it into standby mode most of the time and use the "wake on acceleration event" feature.