Here is some working code.

Pretty printing is left as an exercise:

#!/usr/bin/perl
use strict;
use warnings;
use Data::Dumper;

my %lic_info;
my $pending_product="";
my $pending_user_count=0;

my %actions=(
   "Flexible License Manager" => sub{ 
         @lic_info{qw|DAY DATE TIME|} = $_[0]=~/ on (\w+) (\S+) (\S+)$
+/;
       },
    "Users of " => sub{
        my ($product,$issued, $usecount) = $_[0]=~/Users of (\w+):  \(
+Total of (\d+) license\w? issued;  Total of (\d+) lic/;
        $lic_info{$product}{ISSUED}= $issued;
        $pending_user_count = $lic_info{$product}{USED}= $usecount;
        $pending_product    = $product;
    },
);

my $regex = "(" . join ("|", keys %actions) . ")";


while (<DATA>){
   if ( m/$regex/ ){
      $actions{$1}->($_); # Where the work happens 
   }elsif ($pending_product){
      next if m/^\s+$/;
      next if m/floating license/;
      next if m/\s*\S?$pending_product/;
      push @{$lic_info{$pending_product}{USERS}},
         m/(\S+)/;
      --$pending_user_count or $pending_product = "";
   }
}

print Dumper \%lic_info;

__DATA__
lmutil - Copyright (c) 1989-2009 Flexera Software, Inc. All Rights Res
+erved.
Flexible License Manager status on Wed 1/2/2019 07:00

[Detecting lmgrd processes...]
License server status: 27000@unodecx80
    License file(s) on unodecx80: E:\Program Files (x86)\IBM\RationalR
+LKS\common\rational_server_perm.dat:E:\Program Files (x86)\IBM\Ration
+alRLKS\common\rational_server_temp.dat:

 unodecx80: license server UP (MASTER) v11.10

Vendor daemon status (on unodecx80):

   ibmratl: UP v11.10
Feature usage info:


Users of ClearCase:  (Total of 10 licenses issued;  Total of 1 license
+ in use)

  "ClearCase" v1.00000, vendor: rational
  floating license

    amlove unodecx86 WI_zfTVVG-n7Ph2jhkOo #u#amlove#u# (v1.0) (unodecx
+80/27000 615), start Wed 1/2 6:56 (linger: 1800)

Users of ADALangPack:  (Total of 1 license issued;  Total of 0 license
+s in use)
[download]

OUTPUT:

$VAR1 = {
          'ClearCase' => {
                           'USED' => '1',
                           'USERS' => [
                                        'amlove'
                                      ],
                           'ISSUED' => '10'
                         },
          'ADALangPack' => {
                             'ISSUED' => '1',
                             'USED' => '0'
                           },
          'DATE' => '1/2/2019',
          'DAY' => 'Wed',
          'TIME' => '07:00'
        };
[download]

Update: FYI/FWIW - I was a ClearCase admin in a previous job, decades ago, and I sympathize. That was what taught me perl - so good luck !