You see an the id because it is in the typical location to display an HTML value: between the tags. You need something like this:
ECHO "<option value='" . $row['lecturer_id'] . "'>" . $row['lecturer_lastname']. "</option>";
This will display the name as the option and return the id as the
value of the option. If the value is that in your database table, you can easily pull the requested data.
Update: fixed incorrect quotes.