The Natario warp drive appeared for the first time in 2001.Although the idea of the warp dive as a spacetime distortion that allows a spaceship to travel faster than light predated the Natario work by 7 years Natario introduced in 2001 the new concept of a propulsion vector to define or to generate a warp drive spacetime.Natario defined a warp drivevector for constant speeds in Polar Coordinates but remember that a real warp drive must accelerate or de-accelerate in order to beaccepted as a physical valid model so it must possesses variable speeds.We developed the extension for the original Natario warpdrive vector that encompasses variable speeds.Also Polar Coordinates uses only two dimensions and we know that a real spaceship is a 3D object inserted inside a 3D warp bubble that must be defined in real 3D Spherical Coordinates.In this work we present the new warp drive vector in 3D Spherical Coordinatesfor variable speeds.One the major drawbacks concerning warp drives is the problem of the Horizons(causally disconnected portions ofspacetime) in which an observer in the center of the bubble cannot signal nor control the front part of the bubble.The behavior of a photon sent to the front of the warp bubble in the case of aNatario warp drive with variable velocity and a lapse function is also one of the main purposes of this work.We present the behavior of a photon sent to the front of the bubble in the Natario warp drive in the 1+1 and 3+1 spacetimes with the lapse function using quadratic forms and the null-like geodesics ds^2=0 of General Relativity and the ADM(Arnowitt-Dresner-Misner) formalismequations with the approach of MTW(Misner-Thorne-Wheeler) and Alcubierre.