Filter by category so that only those locations are shown on a leaflet map?

This thread might be useful for you:

Basically, the two approaches I’ve seen people use on this forum involve either using FacetWP (requires some PHP tinkering) or creating links that have URL query parameters like and then using the Url tag’s query attribute to modify your L&L template based on the value of the parameter in the current URL.

I hope that’s helpful for you!