There are a number of different mounts available for the Red One, but the most commonly used is the PL mount, allowing the use of any 35mm lens. The top end manufacturers include Arri, Angenieux and Cooke. There are other lenses available from Nikkon, Canon and from Red Digital Cinema too, but these mostly find their way into the owner/operator market where investment in lenses and lens sets costing tens of thousands of pounds is unusual. As the format can be considered a direct replacement to 35mm film, it would seem unwise to skimp on the most important factor in getting the best images possible to the sensor to be recorded.
The different brands will all have their own associated 'look' based on colour rendition and crispness with some DOPs having a specific preference or requirement. Commonly, the professional lens sets and the Angenieux zooms will all have matching T-stops, making lighting simpler and quicker, without the need for exposure compensation or lighting adjustments.