It is very much possible that pictures will be different but analysis seems to be quite complex.
There are the following phenomena that affect picture:
Light time correction: https://en.wikipedia.org/wiki/Light-time_correction
Aberration of light: https://en.wikipedia.org/wiki/Aberration_of_light
In the framework of SR: - Relativity of simultaneity.
Sure - relativistic length contraction.
If lens is “moving” in the reference frame of the object, lens contracts. Also we have to consider beams of light that RECEIVED when the lens and the object are at points of closest approach.
If object is “moving” in the reference frame of the lens, object contracts. Then we have to consider beams of light that were EMITTED when the object and the lens were at points of closest approach.
There are parallels with measurement of time dilation by means of the
Transverse Doppler Effect: Observer will measure redshift if a source-clock is "moving" in his frame (the clock runs slower) or blueshisft (the clock runs faster) if he is "moving" in the clock's frame. Light time correction and aberration of light also affect measurements in this case.
It is also important to note that the observer in the lens frame can explain that picture doubly, either by ascribing himself state of rest or motion in the object’s frame.
It is very important to consider how the object was highlighted. It is also important to consider aberration of light, since it takes time for the light to reach focal point.
In the framework of Special Relativity beams that were simultaneously emitted (from the different parts of the object) in the object’s frame were not emitted simultaneously in the lens frame, and image will be distorted.
You can find some ideas how these mentioned above factors can affect picture in the papers that consider pictures by simple pinhole camera.