That mountpoint variable is not empty but holds "". Change the if test to

Code:

if [ "$mountpoint" != \"\" ];

and it will fly...


EDIT: BTW, running awk 6 times per line to extract some variables is not the most efficient way to go. The read builtin command can split a line to be read into variables, like

Code:

read NAME TYPE SIZE OWNER GROUP MODE PKNAME MOUNTPOINT

, which will fill all those variables, given the input file is consistently well behaved. Get rid of the prefixes before the equals signs with shell "parameter expansion".
Or, adjust IFS and read the values immediately:

Code:

IFS="$IFS="
read _ NAME _ TYPE _ SIZE _ OWNER _ GROUP _ MODE _ PKNAME _ MOUNTPOINT

The _ is a dummy variable to be discarded.
With a file structure as presented, and using a recent bash with "process substitution", you could do even

Code:

while read LINE
  do    . <(echo $LINE)
        if [ "$MOUNTPOINT" ]
          then  echo -e "Mountpoint:$MOUNTPOINT \n Type:$TYPE"
        fi
  done < $FILE
Mountpoint:/boot 
 Type:part
Mountpoint:/ 
 Type:lvm
Mountpoint:[SWAP] 
 Type:lvm
Mountpoint:/ 
 Type:lvm

, i.e source each line to have it assign all the variables miraculously automatically...