Understanding Lead in a causal system
The voltage of a capacitor can't change instantaneously it needs a certain time. A good way to visualize this behavior is by charging the capacitor with a current source. First we have the current then the voltage builds up. The voltage lags the current (or the current leads the voltage).

For an inductor the current needs some time to build up. A voltage is applied and a current starts to flow. The current lags, the voltage leads.