First off, your code had a sneaky error in which resulted from you not using warnings and strict. Specifically

my $lam_num_ent = $lam_mat_frm -> Entry(),
    -variable=> \$lam_num;
[download]

slips thru and runs without warnings and strict enabled. This results in the entry textvariable not working as expected. It should be

my $lam_num_ent = 
    $lam_mat_frm -> Entry(-textvariable=> \$lam_num);
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To solve the "variable in name" problem, use hashes. In the code below, I only put the Optionmenu widgets in a hash, but for a decent program, you should put all information related to each Optionmenu into a hash, like this for example:

my  %ort_optmen;

$ort_optmen{$num}{'widget'} = whatever
$ort_optmen{$num}{'variable'} = whatever
$ort_optmen{$num}{'options'} = whatever
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That way, all you need to know is $num, and you can get all the information about that Optionmenu widget.

So here is a basic fix to show you the way.

#!/usr/bin/perl
use warnings;
use strict;
use Tk;

# Variables
my $lam_num;
my $ort1;
my $ort2;
my $ort3;

# Main Window
my $mw = new MainWindow;

# Build GUI
my $lam_mat_frm = $mw -> Frame();
my $lam_num_ent = $lam_mat_frm -> Entry(-textvariable=> \$lam_num);

my %ort_optmen; #create hash to hold the optionmenu widgets


$ort_optmen{1} = $lam_mat_frm -> Optionmenu(-options => [qw(-45 0 45 9
+0)],
    -variable => \$ort1);
$ort_optmen{2} = $lam_mat_frm -> Optionmenu(-options => [qw(-45 0 45 9
+0)],
    -variable => \$ort2);
$ort_optmen{3} = $lam_mat_frm -> Optionmenu(-options => [qw(-45 0 45 9
+0)],
    -variable => \$ort3);

for(1..3){
$ort_optmen{$_} -> configure(-state => 'disabled');
}

my $lam_data_button = $lam_mat_frm->Button(-text=>"Input Laminate Data
+",
    -command=> \&input_lam_data);

# Geometry Management
$lam_mat_frm -> grid(-row=>1, -column=>1, -columnspan=>2);
$lam_num_ent -> grid(-row=>1,-column=>1);

$ort_optmen{1} -> grid(-row=>2,-column=>1);
$ort_optmen{2} -> grid(-row=>3,-column=>1);
$ort_optmen{3} -> grid(-row=>4,-column=>1);

$lam_data_button -> grid(-row=>5,-column=>1);

MainLoop;

sub input_lam_data {

print "$lam_num\n";

#reset them all off to begin with
foreach (1..3){
$ort_optmen{$_} -> configure(-state => 'disabled');
 }

# you need to do some valid range checking for $lam_num here
# I leave that to you

foreach my $num (1..$lam_num){
    $ort_optmen{$num} -> configure(-state => 'normal'); 
      }
}
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</c>