What you can do, if you have sufficient rights (otherwise, ask your admin to do it), is to add the following line into sudoers file:

Defaults:your_notes_user !requiretty

Replace your_notes_user with username that can run notes, save it and that is it.

How do you do that?

1. Login to your linux machine
2. In console type visudo and press enter
3. Edit the file by pressing either i or a vi command
4. Go to the end of the file and add above mentioned line
5. Save the file using :wq

#!/bin/bash
#
# /etc/init.d/domino
#
### BEGIN INIT INFO
# Provides:          Domino
# Required-Start:    $syslog $remote_fs $network
# Required-Stop:     $syslog $remote_fs $network
# Default-Start:     3 5
# Default-Stop:      0 1 2 6
# Short-Description: Domino providing IBM Lotus Domino Server
# Description:       Start Domino to provide an IBM Lotus Domino Server
### END INIT INFO
# 

. /etc/init.d/functions
DATADIR=/opt/ibm/notesdata
RETVAL=0

start() {
	echo -n "Starting Domino Server"
	sudo -u notes /opt/ibm/lotus/bin/server "=$DATADIR/notes.ini" -jc -c &
	RETVAL=$?

	# Remember status and be verbose
	echo
	[ $RETVAL -eq 0 ]
	return $RETVAL
}

stop() {
	echo -n "Shutting down Domino Server"
	sudo -u notes /opt/ibm/lotus/bin/server "=$DATADIR/notes.ini" -q
	RETVAL=$?

	# Remember status and be verbose
	RETVAL=0   # have to force this since since there's no way of really
                        # knowing
	echo
	[ $RETVAL -eq 0 ]
	return $RETVAL
}

restart() {
	# Stop the service and regardless of whether it was running or not,
        # start it again.
	stop
	start
}

case "$1" in
    start)
	start
	;;
    stop)
	stop
	;;
    restart)
	restart
	;;
    *)
 echo "Usage: $0 {start|stop|restart}"
 exit 1
 ;;
esac
exit $RETVAL