public static Task<List<FeatureLayer>> GetHistoricParcelLineLayerByTypeNameAsync( 
   ParcelLayer parcelLayer,
   string typeName
)

private async Task<string> GetParcelTypeNameFromFeatureLayer(ParcelLayer myParcelFabricLayer, FeatureLayer featLayer, GeometryType geomType)
{
  if (featLayer == null) //nothing to do, return empty string
    return String.Empty;
  IEnumerable<string> parcelTypeNames = await myParcelFabricLayer.GetParcelTypeNamesAsync();
  foreach (string parcelTypeName in parcelTypeNames)
  {
    if (geomType == GeometryType.Polygon)
    {
      var polygonLyrParcelTypeEnum = await myParcelFabricLayer.GetParcelPolygonLayerByTypeNameAsync(parcelTypeName);
      foreach (FeatureLayer lyr in polygonLyrParcelTypeEnum)
        if (lyr == featLayer)
          return parcelTypeName;

      polygonLyrParcelTypeEnum = await myParcelFabricLayer.GetHistoricParcelPolygonLayerByTypeNameAsync(parcelTypeName);
      foreach (FeatureLayer lyr in polygonLyrParcelTypeEnum)
        if (lyr == featLayer)
          return parcelTypeName;
    }
    if (geomType == GeometryType.Polyline)
    {
      var lineLyrParcelTypeEnum = await myParcelFabricLayer.GetParcelLineLayerByTypeNameAsync(parcelTypeName);
      foreach (FeatureLayer lyr in lineLyrParcelTypeEnum)
        if (lyr == featLayer)
          return parcelTypeName;

      lineLyrParcelTypeEnum = await myParcelFabricLayer.GetHistoricParcelLineLayerByTypeNameAsync(parcelTypeName);
      foreach (FeatureLayer lyr in lineLyrParcelTypeEnum)
        if (lyr == featLayer)
          return parcelTypeName;
    }
  }
  return String.Empty;
}