NTLM authentication for http monitor for sharepoint 2013 webserver

You'll need to construct an external monitor: https://devcentral.f5.com/articles/ltm-external-monitors-the-basics

Here's an example of an external monitor for Exchange Autodiscover that uses NTLM:

!/bin/sh
 These arguments supplied automatically for all external monitors:
 $1 = IP (nnn.nnn.nnn.nnn notation)
 $2 = port (decimal, host byte order)

 This script expects the following Name/Value pairs:
  USER  = the username associated with a mailbox
  PASSWORD = the password for the user account
  DOMAIN = the Windows domain in which the account lives
  EMAIL = the email address associated with the user mailbox

 Remove IPv6/IPv4 compatibility prefix (LTM passes addresses in IPv6 format)

NODE=`echo ${1} | sed 's/::ffff://'`
if [[ $NODE =~ ^[0-9]{1,3}.[0-9]{1,3}.[0-9]{1,3}.[0-9]{1,3}$ ]]; then
     node is v4
    NODE=${NODE}
else
     node is v6
    NODE=[${NODE}]
fi
PORT=${2}
DIR="http://schemas.microsoft.com/exchange/autodiscover/outlook"
PIDFILE="/var/run/`basename ${0}`.my_new_iapp_test_2010_${USER}_${NODE}_ad.pid"
XML1=$( cat<
EOF
)
XML2=$( cat<${DIR}/responseschema/2006a
EOF
)
XMLFULL=${XML1}${EMAIL}${XML2}
RECV=''
ADSURI='/Autodiscover/Autodiscover.xml'
 kill of the last instance of this monitor if hung and log current pid
if [ -f $PIDFILE ]
then
   echo "EAV exceeded runtime needed to kill ${NODE}:${PORT}" | logger -p local0.error
   kill -9 `cat $PIDFILE` > /dev/null 2>&1
fi
echo "$$" > $PIDFILE
curl-apd -g -s --ntlm -k -X POST -H 'Content-Type: text/xml; charset=utf-8' -d "${XMLFULL}" -u ${DOMAIN}\\${USER}:${PASSWORD} http://${NODE}${ADSURI} | grep -i "${RECV}" > /dev/null 2>&1
STATUS=$?
rm -f $PIDFILE
if [ $STATUS -eq 0 ]
then
    echo "UP"
fi
exit