To avoid the loop, put the conditions given by roboticus, above, into the block of a grep:

#! perl
use strict;
use warnings;
use Data::Dump;

my %LPAR_config =
(
    lpar1 =>
    {
        profile1 => {},
        profile2 => {},
        frame    => 'frame1',
        lpar_id  => '1',
    },

    lpar2 =>
    {
        profile1 => {},
        profile2 => {},
        frame    => 'frame1',
        lpar_id  => '2',
    },

    lpar3 =>
    {
        profile1 => {},
        profile2 => {},
        frame    => 'frame2',
        lpar_id  => '1'
    },

    lpar4 =>
    {
        profile1 => {},
        profile2 => {},
        frame    => 'frame2',
        lpar_id  => '2',
    },
);

my @matches = grep { $LPAR_config{$_}->{frame  } eq 'frame2' &&
                     $LPAR_config{$_}->{lpar_id} eq '1' } keys %LPAR_c
+onfig;
dd @matches;
[download]

Output:

 1:43 >perl 560_SoPW.pl
"lpar3"

 1:44 >
[download]

Hope that helps,