Are lab diamonds real diamonds?

Yes! There is no such thing as a fake diamond. There are just diamond simulants and diamonds.

Diamond Simulants

Diamond simulants are cheap facsimiles of diamonds such as cubic zirconias, moissanite, white topaz, and yttrium aluminum garnet (YAG). Diamond simulants do not have the same chemical composition, physical properties, or optical behavior of a diamond. Every known diamond simulant is weaker and softer than a diamond.

Ada Diamonds refuses to sell diamond simulants, as diamond simulants are not diamonds.

Diamonds

Diamonds are a crystal of carbon and can either be naturally formed by high pressure and temperature underneath the surface of the Earth, or they can be created above the Earth in what can only be described as a paragon of human achievement.

The FTC defines a diamond as follows: A diamond is a mineral consisting essentially of pure carbon crystallized in the isometric system.

Chemical Definition of a Diamond:
A Cubic Crystal Allotrope of Carbon

Diamonds are merely one form of carbon: a cubic crystal structure of carbon. Other known forms of carbon are graphite, carbon black (coal), carbon nanotubes, graphene, and carbon nanofoam, which is one of the lightest known solid materials. These forms of carbon are known as allotropes.