All a mode or scale is, is what quality each degree has against a given root. The only difference between the major scale and the lydian mode is the major scale's fourth degree is a perfect fourth above the root. In the lydian the fourth degree is an augmented fourth above the root. So the lydian sound is basically this interval and how it interacts with the key tone. Otherwise there the same scale.

Playing or thinking C lydian when the key is G major is thinking too much. It's the same scale. ALl scales or modes are altered major scales. So playing a mode is just playing an altered scale over a given key. So if the harmony is in G major, using G lydian for the solo is modal. Using C lydian is nothing more than playing the G major scale. See what I mean. Modally writting is using contrast.