If you want to focus the light of a 1 mm wide emitter to 0.5 mm wide spot, you can achieve that by making the lens to move towards the emitter. (at some fraction of speed of light)
In an electron gun we want to make the initial random speeds of the electrons very low, by making the electrode as cool as possible.
Then we could accelerate the magnetic lens towards the electrons, but it's easier to accelerate the electrons towards the magnetic lens. Anyway, the principle of relativity says we can achieve the same focusing effect either way.
So in this little analogy thermal electrons are analogous to thermal photons, and the speed of the lens relative to the light emitter is analogous to the speed of the magnetic lens relative to the electron emitter.
A quick course in information theory and thermodynamics of lenses and screens:
A lens-screen combination converts direction information into position information, an eye is an example of this.
A lens-screen combo converts order in the directions of particles into order of marks on the screen.
There are easy ways to remove disorder in directions of particles:
a: let the particles with more aberrant directions leave the group
b: accelerate all particles the same amount
Lenses are used to produce positionally ordered (narrow) beams, because it is easy to produce directionally ordered beams.