Carefully said by using the word, "could". I have seen a few people with LifeProof cases for the 4/4S with a screen protector and they show off their waterproofed cases without ever having an issue.
LifeProof's official FAQ answer is as follows:
and
This FAQ
LifeProof's official FAQ answer is as follows:
Our LifeProof cases have a durable and scratch resistant screen cover for your device, which also has an anti-glare coating. We do not advise any additional screen protectors placed on the device because it may negatively affect the touchscreen sensitivity as well as the optical clarity of your device.
and
This FAQ
LifeProof Cases are created with dimensions to specifically fit the device itself. Products that change the dimensions of the LifeProof case would not be compatible with our case. While the Zagg InvisibleSHIELD does not affect the dimensions of the iPhone, it introduces a thin layer over the screen which, when coupled with the LifeProof case, may affect touchscreen sensitivity as well as the optical clarity. For this reason it is not recommended that you use an InvisibleSHIELD with your LifeProof case - the case will keep your phone more than safe enough!