I suspect that you forgot the s modifier for the regex.

#!/usr/bin/perl
my $search = '10.2.56.75'; # the ip we are looking for, could pull fro
+m @ARGV
my $data;

{ # slurp in all of the info in the DATA section
  local $/ = undef;
  $data = <DATA>;
}

my ($lease) = $data =~ /lease $search {(.+?)}/is; # find the first mat
+ch

print $lease,"\n";

__DATA__
lease 10.2.56.40 {
        starts 3 2003/08/20 10:37:28;
        ends 3 2003/08/20 22:37:28;
        hardware ethernet 00:20:af:52:12:0f;
        uid 01:20:af:52:12:0f;
        client-hostname "Telephone";
}
lease 10.2.56.75 {
        starts 3 2003/08/20 09:57:11;
        ends 3 2003/08/20 21:57:11;
        hardware ethernet 00:ef:18:ae:52:83;
        uid 01:00:ef:18:ae:52:83;
        client-hostname "beast";
}
lease 10.2.56.77 {
        starts 2 2003/08/19 21:13:05;
        ends 3 2003/08/20 21:13:05;
        hardware ethernet 00:02:95:9b:78:18;
        uid 01:02:0b:95:9b:78:18;
}
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