While there's nothing wrong with your $LINE_PATTERN regex I think it would be simpler to keep the record and field/value processing separate. To my eye it looks tidier and easier to maintain but others may disagree.

use strict;
use warnings;

use Data::Dumper;

my $app_text =
   qq{one:partridge\ntwo:\nturtle doves\nthree:french hens\n};

my %fvPairs =
   map { split m{:\n?} }
   map { split m{(?<!:)\n} }
   $app_text;

print Data::Dumper->Dumpxs( [ \ %fvPairs], [ q{*fvPairs} ] );
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produces ...

%fvPairs = (
             'three' => 'french hens',
             'one' => 'partridge',
             'two' => 'turtle doves'
           );
[download]

Cheers,

JohnGG