It is hard to tell from your picture, but is that a rolled edge of a spa/pool made of pebble that is not submerged?

Typically you want plaster/pebble submerged which I suspect is the issue here. I'll let others chime in on how/if you can repair it.
 
Can this crack be repaired by a neophyte?

I don't think any repair will ever look good.

Why do you think it needs to be repaired?

How would the neophyte repair it?

That is a typical crack from plaster being allowed to dry out. Plaster is made to be submerged and kept wet. It is a poor finish for above water.
 
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