public void Save( 
   string layerXFilePath
)

{
    //Note: Call within QueuedTask.Run()
    var lyrDocFromLyrxFile = new LayerDocument(@"d:\data\cities.lyrx");
    var cimLyrDoc = lyrDocFromLyrxFile.GetCIMLayerDocument();

    //modifying its renderer symbol to red
    var cimSimpleRenderer = ((CIMFeatureLayer)cimLyrDoc.LayerDefinitions[0]).Renderer as CIMSimpleRenderer;
    cimSimpleRenderer?.Symbol.Symbol.SetColor(new CIMRGBColor() { R = 255 });

    //optionally save the updates out as a file
    lyrDocFromLyrxFile.Save(@"c:\data\cities_red.lyrx");

    //get a json representation of the layer document and you want store away...
    var aJSONString = lyrDocFromLyrxFile.AsJson();

    //... and load it back when needed
    lyrDocFromLyrxFile.Load(aJSONString);
    cimLyrDoc = lyrDocFromLyrxFile.GetCIMLayerDocument();

    //create a layer and add it to a map
    var lcp = new LayerCreationParams(cimLyrDoc);
    var lyr = LayerFactory.Instance.CreateLayer<FeatureLayer>(lcp, map);
}

{
    LayerDocument layerDocument = new LayerDocument(layer);
    //Note: Run within QueuedTask
    layerDocument.Save(@"c:\Data\MyLayerDocument.lyrx");
}