How to manually set a color of a LineSeries via json config in amcharts v4?

You almost had it. You have to set the stroke at the top-level of the LineSeries definition (see JSON tab in the docs):

"series": [{
  "type": "LineSeries",
  "stroke": "#567890",
  // ...
},
// ...
]

JSON values line up very closely to the declarative syntax, hierarchy-wise. You can find more full JSON examples in the github repo.