var map = (OpenLayers.Map ); // your map reference
var layerswitcher = (OpenLayers.Control.LayerSwitcher) // layer swicher control reference
OpenLayers.Lang[OpenLayers.Lang.getCode()]['Base Layer'] = "My base label";
OpenLayers.Lang[OpenLayers.Lang.getCode()]['Overlays'] = "My over label";
// remove current instance of layers switcher from map if attached.
map.removeControl( layerswitcher );
map.addControl( new OpenLayers.Control.LayerSwitcher( { /* options here */ } ) );
Adicionalmente, podría probarse también:
layerSwitcher = map.getControlsByClass("OpenLayers.Control.LayerSwitcher")[0];
layerSwitcher.baseLbl.innerText // (returns "Base Layer")
layerSwitcher.dataLbl.innerText // (returns "Overlays")
// asignando nuevo texto
layerSwitcher.baseLbl.innerText = "YOUR NEW TEXT"
layerSwitcher.dataLbl.innerText = "YOUR NEW OVERLAY TEXT"