Below is the Superintendent's Compendium section on sUAS operations at Lake Mead. It clearly is legal to fly at that designated location, but flying from that location out over the lake is a different matter.
Firstly, the lake is 1 km from the field, and so it's very dubious that you could reasonably claim VLOS. While plenty of recreational pilots stretch that rule to extreme lengths, I would definitely not recommend it in your job.
Secondly - while NPS doesn't have jurisdiction over the airspace, you would be flying from their field, and one of their conditions is that the flight is restricted to the boundaries of the RCMA field. Would that stand up in court? Hard to say, but not something I would want to test.
Other options - you could probably get some good aerial views of the lake from 400 ft above the field, but maybe that's not really what you are looking for. Alternatively, you can get authorization to fly from the superintendent, and working for an accredited TV station that may be something that they would be willing to consider.
Definition:
The term “unmanned aircraft” means a device that is used or intended to be used for flight in the air without the possibility of direct human intervention from within or on the device, and the associated operational elements and components that are required for the pilot or system operator in command to operate or control the device (such as cameras, sensors, communication links). This term includes all types of devices that meet this definition (e.g. model airplanes, quadcopters, drones) that are used for any purpose, including for recreation or commerce.
Closure:
The launching, landing or operating of an unmanned aircraft from or on lands and waters administered by the National Park Service within the boundaries of Lake Mead National Recreation Area is prohibited except as approved in writing by the Superintendent.
Exemption:
Since 1992, a historical establishment of the use of model aircrafts (aka Radio Controlled Model Aircrafts (RCMA)) was authorized at Lake Mead National Recreation Area. Only the use of RCMA at the designated area will continue to be allowed. The designated area is signed as “Radio Control Model Aircraft Field” and is located on the Frontage Road approximately .60 miles from Hemenway Drive in the Boulder Beach area. The radio control model aircraft field is approximately .36 square miles. This area is used by hobbyist and recreational users. All flights will be below 400 feet Above Ground Level (AGL), and line-of-sight control. Historic use of RCMA has had minimal impact to the general public and park resources and values. The radio controlled model aircraft is restricted within the designated field. Flying over the adjacent campground, trailer park and lake users is prohibited.
Determination: This closure is to prevent possible conflicts, maintain public health and safety, and prevent any unacceptable impacts on park resources and values.