K0:
It's good that you're concatenating like that though. It helps for when you want to validate or ensure that hacking attempts aren't being tried. Concatenation is the first step. The next is to actually try and prohibit the hacking from affecting you with [man]mysql_real_escape_string/man around each $_POST[] item....
But, if you don't like concatenation (like some don't), you could do it this way:
<?php
$uname = mysql_real_escape_string($_POST['username']);
$skid = mysql_real_escape_string($_POST['SK_ID']);
$lrole = mysql_real_escape_string($_POST['lecturer_role']);
// Now, all our strings are most likely free of hacking issues (no guarantee)
$query = "SELECT lecturer_role, SK_ID, LK_ID
FROM student_project
WHERE LK_ID='$uname'
AND SK_ID='$skid'
AND lecturer_role='$lrole'";
$result = mysql_query($query);
Now, the reason the query is broken up on lines is because when you run the mysql_error() function, it gives a line number. Break the query up on lines, you can quickly find it. It's most helpful on long complicated queries.