From the Process
javadoc: http://docs.oracle.com/javase/7/docs/api/java/lang/Process.html
By default, the created subprocess does not have its own terminal or console. All its standard I/O (i.e. stdin, stdout, stderr) operations will be redirected to the parent process, where they can be accessed via the streams obtained using the methods getOutputStream(), getInputStream(), and getErrorStream(). The parent process uses these streams to feed input to and get output from the subprocess.
You can get the OutputStream from the Process and write to it what you would normally type directly in to the console when running SqlLite interactively.
OutputStream os = process.getOutputStream();
BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(os));
bw.write("SELECT * FROM clients;");
bw.newLine();
bw.flush();
Then read the InputStream like you do already, it should have the output you would normally see when running SqlLite interactively.