Does gravitational lensing cause the speed of light to change?
Gravitational lensing does not alter the speed of light in space.
Gravitational lensing is analogous to the dispersion or convergence of light through optical lenses. Gravitational lensing is dependent on the mass of the lens and proximity to the light source.
Four dimensional time-space bending is described here:
When we observe far-away objects in space, we are not seeing them as they are now, but as they were many hundreds or thousands of years ago. It has taken that long for the light from the object to reach us. During that time, the light will probably have undergone significant changes.
When light travels through space, it may be bent out of its normal straight line trajectory. This can result in the source object looking brighter or larger, or being duplicated, or appearing as a cluster with halos around it.
The halo effect is described here:
The bending occurs when the light contacts intervening bodies or cosmic dust that shifts the light path. The light may diverge so we cannot see the source, or it may converge to make the source brighter or bigger in appearance.
The amount of the light bending varies infinitely with the mass of the object(s) in the light path, and where they are located relative to the source. But, statistical averages of observations can be used to provide useful information on closely monitored lenses.
No, light always travels at the speed of light in a vacuum.
Gravitational lensing is the effect where light from a distant object gets bent around massive objects making the position of the object appear to shift.
The term gravitational lensing is actually confusing a the effect is completely different from that of an optical lens. An optical lens work using refraction. When light enters a transparent medium it slows down changing direction in the process.
Massive objects cause the fabric of 4 dimensional spacetime to curve. Light always follows a geodesic which is the 4 dimensional equivalent of a straight line. When light passes by a massive object it follows the curvature of spacetime near the object. It doesn't change speed as it always travels at the speed of light in a vacuum.
The amount that a massive object bends light is related to how much the object causes spacetime to curve. The amount spacetime is curved is dependent on the mass and energy of the object as described by Einstein's field equations.