Lab diamonds, just like their mined counterpart, include the option to go with a colored diamond. The amazing colors, as shown in this blue cushion center diamond, undergo special treatment whether mined or lab grown.
A mined blue diamond is incredibly rare, and incredibly expensive. Compare that to a lab grown blue diamond, and the difference in cost is significant.
In order to "create" a colored lab diamond, the process involves a treatment that irradiates the diamond using high energy electrons, creating new atoms in the diamonds chemical make up that absorbs light in a blue range (or pink, or other colors offered).
Maintaining the color does involve keeping the stone away from very high heat, as it can impact the depth of color. The good news is that a stone can be re-irradiated, if a rare event causes any fading.
Shown is a cushion cut irradiated lab diamond, with a pear shape surround, or halo.