Does lowering temperature of a gas make it easier to compress?
Compressing a gas by applying an external force means to work against the force the gas exerts on the walls of its container, i.e. its pressure.

The definition of compressibility

$$\beta = -\frac{1}{V}\frac{\partial V}{\partial p} \tag{1}$$

for an ideal gas with the well-known equation of state

$$p V = n R T \tag{2}$$

gives

$$\beta = -\frac{1}{V}\frac{\partial V}{\partial p} = \frac{1}{V} \frac{n R T}{p^2} = \frac{1}{p} \tag{3}$$

which is independent of the temperature $T$.

For non-ideal gases there will be higher order terms that also depend on temperature.

It is also worth noting that at the critical point the compressibility of a real gas is infinite. So if you are below the critical temperature you will be able to compress the gas more easily at a state (the critical point) with higher temperature.