How can I replace a ceiling light and repair the surrounding plaster?
You really don't want to disturb the lath with a light fixture.  The plaster is fragily 'keyed' into the gaps between the lath.  The weight of the light must connect to structure.  Ideally, the light fixture should be independent of the plaster.

The plaster must be 'quietly' cut back.  I use a continuous rim diamond wheel (4 1/2 inch on an angle grinder) to cut the plaster. 

You need to carefully cut back the exposed lath and use a 'feeler' probe to find how far away the joists are, to each side.

You should use the Polyfilla powder for interiors, powered gypsum joint compound (with plaster-of-paris for setting) or an authentic lime based plaster (for best compatibility).

Traditionally plaster involves a brown coat, a scratch coat and a finish coat.  Metal lath is useful for making repairs to existing ceilings.