When I go to http://gis.fws.gov/FWSLands_Mapper_Lite/index.html?layernum=0&searchfield=LIT&searchtext=KLP I got to where I want to be. Yet when I go to http://fws.maps.arcgis.com/home/webmap/viewer.html?webmap=c09a9b32db9e45179dd29be2e253da52&layernum=... it doesn't take me there. When I go to the rest service for the latter (http://gis.fws.gov/arcgis/rest/services/FWSCadastral_Internet/MapServer/layers) I see that the first layer has field called LIT so it seems those parameters ought to work.
Alan,
Custom widget url parameters are not supported when using the AGOL version of WAB.