In terms of performance, the single most important change to be done is to use a hash enabling direct lookup instead of an array to store ther $xref data, as already suggested by Corion. Depending on the size of the $xref file, this change alone can make your program thousands times (or even much more) faster.

A few other changes might improve your code. Insert these pragmas:

use strict;
use warnings;
[download]

at the top of all your Perl programs, and declare your variables (with the my keyword).

You don't need to store your customer file into an array (@lines) and then read the array, this leads you to process twice the same data, which is a waste of time. Do your checks when reading your customer file line by line;

Use the three-argument syntax of open and use lexical file handles (see examples below).

This could lead to something like this (untested):

use strict;
use warnings;
# Read the values from XREF into a hash
my $xref = "input_file.txt";  # put here real filename
open my $XREF, "<", $xref or warn "Could not open $xref $!";  # A more
+ detailed message can sometimes be useful
my %xreflines =  map { chomp; $_ => 1 } grep /\S/, <$XREF>;     # popu
+lating the hash with the content of the xref file
close $XREF;

my $goodfile = ...;                                 # insert the name 
+of the output file here
open my $XFILE, ">>", $goodfile or warn "Could not open $goodfile $!";

my $outfile = ...;                                  # insert the name 
+of the customer file here
open my $CUSTOMERFILE, "<", $outfile or warn "Could not open $outfile 
+$!";
while (my $line = <$CUSTOMERFILE>) {
    my ($dist, $cust) = (split /;/, $line)[0,1];    # no need to chomp
+ the fields, there are other fields afterwards in the line
    my $key = "$dist$cust";                         # Building the loo
+kup key
    unless (exists $xreflines{$key}) {              # hash lookup
        print $XFILE "$line";                       # printing the lin
+es whose ID is not found in the cross ref file
    }
}
close $XFILE;
close $CUSTOMERFILE;
[download]

Update: removed some extra quote marks left out from the OP code when changing the open syntax. Thanks to choroba for pointing out.

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