public bool IsLinkChartView {get;}

var mv = MapView.Active;
// check the view
var isLinkChartView = mv.IsLinkChartView;

// or alternatively get the map and check that
var map = MapView.Active.Map;
// check the MapType to determine if it's a link chart map
var isLinkChart = map.MapType == MapType.LinkChart;
// or you could use the following
// var isLinkChart = map.IsLinkChart;

var mapPanes = FrameworkApplication.Panes.OfType<IMapPane>().ToList();
var mapPane = mapPanes.FirstOrDefault(
    mp => mp.MapView.IsLinkChartView && mp.MapView.Map.Name == "Acme Link Chart");
var lcMap = mapPane.MapView.Map;