Phase shift in an LCR circuit
The voltage/current phase relationship is true for each component individually.

In a series RLC circuit, they all share current. This means the total observed terminal voltage is the sum of all the individual voltages. The inductor voltage is always opposed to the capacitor voltage, they are always 180 degrees apart from each other.

At low frequencies, where the capacitor voltage is high and so dominates the total, and the voltage will lag the current. At high frequencies, where the inductor voltage is high, the current will lag the voltage. 

At one specific intermediate frequency where the magnitude of the capacitor voltage and the inductor voltage are equal, they will cancel each other out. Voltage and current will now be in phase, voltage will be a minimum, and the circuit is said to be in resonance.

You can go through a similar line of reasoning for parallel connected components. These share the same voltage, and so the currents through the individual components add up to make the total. At resonance the total current is now a minimum.