50,000 fps = 20 μs/frame. Your pulse is only one thousandth of that. A camera sensor will integrate the light input over the duration of the exposure but I suspect that you would have to run at high gain and that noise might be a problem.
I am wondering if it is practical to try and focus the beam onto a high speed optical sensor array (capturing 50,000 fps) with some kind of lens arrangement ...
Figure 1. Object, lens and image. Stemmer Imaging.
You won't be focusing the beam into a sensor or it will be destroyed (and the problem of placing the lens in the right place). Instead you will focus an image of the target and illuminated spot onto the sensor. This is how a film or digital camera works. Some of the light reflected by the subject is focused onto the film or sensor matrix.
... and performing computer analysis on the resulting feed.
That sounds reasonable - once you've got a decent image.
... how does one go about selecting suitable optical elements for such a setup?
It's basically a camera lens. There are good catalogues in paper and online form from companies such as Edmund Scientific and Stemmer Imaging. These often have good diagrams which are highly educational.
You don't say what the laser power is or what the target is but since it's visible green I'm wondering if you can run at reduced power for a long time to make it easy for the image capture.