Android - save value on LocalStorage before WebView.loadUrl()

You can use WebViewClient.onPageStarted() for this.

webView.setWebViewClient(new WebViewClient() {
    @Override
    public void onPageStarted(WebView view, String url, Bitmap favicon) {
        super.onPageStarted(view, url, favicon);
        String js = "window.localStorage.setItem('key', 'value');";
        if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.KITKAT) {
            webView.evaluateJavascript(js, null);
        } else {
            webView.loadUrl("javascript:" + js);
        }
    }
});

What you can do is set a redirect into the javascript to the actual url and load the javascript plus redirect using webview.loadData().

 String injection = "<html><head><script type='javascript'>LocalStorage.set('namespace', 'key', 'value');window.location.replace('YOUR_URL_HERE');</script></head><body></body></html>";
 webview.loadData(injection, "text/html", null); 

Be aware though that you might need to save that to a file first before it works: see How to load a javascript redirect into android webview?