Impedance phase angle relative to?
Edited to account for my random inability to read the question correctly.

An impedance is not normally described as lagging. The current is described as lagging/leading the voltage applied.

However, in the capacitance example, the current leads by 90 degrees and this forces the impedance to have a negative phase angle because if the angle in the denominator is positive it becomes equivalent to a negative angle in the numerator.

An easy way to remember is CIVIL - in a Capacitor, I leads V and V leads I in an inductor.