Check if a row exists using old mysql_* API

$result = mysql_query("select if(exists (SELECT * FROM  preditors_assigned WHERE lecture_name='$lectureName'),'Assigned', 'Available')");

Easiest way to check if a row exists:

$lectureName = mysql_real_escape_string($lectureName);  // SECURITY!
$result = mysql_query("SELECT 1 FROM preditors_assigned WHERE lecture_name='$lectureName' LIMIT 1");
if (mysql_fetch_row($result)) {
    return 'Assigned';
} else {
    return 'Available';
}

No need to mess with arrays and field names.

This ought to do the trick: just limit the result to 1 row; if a row comes back the $lectureName is Assigned, otherwise it's Available.

function checkLectureStatus($lectureName)
{
    $con = connectvar();
    mysql_select_db("mydatabase", $con);
    $result = mysql_query(
        "SELECT * FROM preditors_assigned WHERE lecture_name='$lectureName' LIMIT 1");

    if(mysql_fetch_array($result) !== false)
        return 'Assigned';
    return 'Available';
}

Use mysql_num_rows(), to check if rows are available or not

$result = mysql_query("SELECT * FROM preditors_assigned WHERE lecture_name='$lectureName' LIMIT 1");
$num_rows = mysql_num_rows($result);

if ($num_rows > 0) {
  // do something
}
else {
  // do something else
}