[Nor Cal ZL1]

I'm not sure at which lowering amount the C5 geometry goes opposite, perhaps some of the vendors can provide that. I'll try to explain what happens when it passes the point of going too low.

Normally the lower balljoint is lower than the mounting point of the control arm. Using a right hand turn here is how the geometry works.

The driver side compresses and the movement arch forces the balljoint more outwards and increases the negative camber gain= more negative camber and a larger tire contact patch.
The passenger side will act the opposite and pull the ball joint inwards and decrease the negative camber gain to a more positive= larger contact patch.

Suspension that has equal or the balljoint end is higher than the mounting point will act as this. This is the exact opposite of what you want to happen.
The drivers side control arm will arch towards the cars center and pull the balljoint inwards decreasing the negative camber gain, removing increased contact patch opportunity.
The passenger side control arm will arch away from the cars center, and push the balljoint outward increasing the negative camber gain, removing increased contact patch opportunity.

Race cars have custom suspension, or dropped spindles to get the height.
As long as the geometry is not compromised, lowering will work fine

Edit just went and look at the front suspension of the ZL, and personally I would not go more than 1/2 to 3/4 lower. At 1 inch the control arm would be parallel with the body mount.