Can a lighting transformer be used to power a pump?
A lighting transformer might just be a 230V AC (or 110V AC) to 12V AC transformer and AC won't work on a DC pump, it will rotate back and forth with 50 or 60 Hz.

So a SMPS will probably work. You can try if you have an old PC PSU lying around, those are SMPS as well.

As pointed out by Brian Drummond in the comments, if your lighting transformer is just an AC type (those will be pretty heavy) you can try and put a bridge rectifier with enough current handling capability (at least 5A) at the output of the transformer and hook up the pump to the output of the bridge rectifier.

The rotor should keep rotating smoothly as it will store momentum and bridge over those points where the output has too little voltage to drive the pump.