The best way of catching errors in a DBI operation is through eval.

my $dbh = DBI->connect("dbi:driver:database",
    "user","password", 
    {RaiseError=>1, PrintError=>0})
      or die "can't connect ($DBI::errstr)\n";

my $sth;
eval {
    $sth = $dbh->prepare( $sql );
    $sth->execute;
};

if ($@) {
     print "There was an error ($DBI::errstr)\n";
     # do something appropriate
}
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Notice that RaiseError must be on, to be sure it will raise an exception in case of error. The DBI docs have all the details of this procedure.

I believe you would benefit from a walk through our Tutorials about database programming. Start with this one.

As a side note, instead of using "INSERT INTO t1 (lsname) VALUES ('$lsname')"; consider the placeholder mechanism, which will make sure that your field is properly quoted.

my $sql = "INSERT INTO t1 (lsname) VALUES ( ? )";
my $sth;
eval {
    $sth = $dbh->prepare( $sql );
    $sth->execute ($lsname);
};

if ($@) {
     print "There was an error ($DBI::errstr)\n";
     # do something appropriate
}
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$sth->execute() || die("Divide By Cucumber Error\n");

On another note, you really should be using placeholders rather than interpolating $lsname directly into your SQL. Consider what would happen if the variable contained an apostrophe. Or if it contained foo');update t1 set lsname='you are owned