Ok, that makes it easy to approach.
while($row = mysql_fetch_array($result)){
if(strpos($row['link'], 'lakesideca.com') === false) {
$linkTarget = '_blank';
} else {
$linkTarget = 'container';
}
echo "<font color= maroon><font size=2>";
echo $row['event'];
echo "</font>";
echo "<font color= black><font size=2>";
echo $row['article'];
echo "</font>";
echo "<a target=\"$linkTarget\" href='$row[link]'> Go there[/url]";
echo "</font>";
echo "";
echo "";
}
The if statement simply checks if the string "lakesideca.com" (internal links) is in the link field, and if so sets $linkTarget to "container", otherwise it must be external so it get set to _blank.
That should get you on your way.
caution: quick off-the-cuff untested code