Should "LL" result in

THAETURQU                .LLL..RRR                HA,AE
JURYATAUTIOPW            .LLL...LL.RRR            UR,RY,UT
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL  WQ,QN,NQ,MN,NH,HF
[download]

or

THAETURQU                .LLL..RRR                HA
JURYATAUTIOPW            .LLL...LL.RRR            UR,UT
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL  WQ,NQ,MN,HF
[download]

kennethk assumed the latter. The following handles the former:

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

my @patterns = qw(
    .LLL
    LLLL
    .RRR
    RRRR
    LL
);

chomp( my @file = <DATA> );

for my $pat (@patterns) {
    print("pattern = $pat\n");

    our $string;
    our @matches;
    my $re = do {
        use re 'eval';
        qr/
            \Q$pat\E
            (?{
                my $start = $-[0];
                my $end   = $+[0];
                push @matches, substr($string, $start, $end - $start);
            })
            (?!)
        /x
    };

    for my $line (@file) {
        (local $string, my $mask) = split(/\s+/, $line, 2);
        local @matches;
        $mask =~ $re;
        local $" = ",";
        print "$line\t@matches\n";
    }

    print("\n");
}

__DATA__
THAETURQU                .LLL..RRR
JURYATAUTIOPW            .LLL...LL.RRR
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL
[download]

pattern = .LLL
THAETURQU                .LLL..RRR                THAE
JURYATAUTIOPW            .LLL...LL.RRR            JURY
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL  OWQN,WMNH

pattern = LLLL
THAETURQU                .LLL..RRR
JURYATAUTIOPW            .LLL...LL.RRR
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL  WQNQ,MNHF

pattern = .RRR
THAETURQU                .LLL..RRR                URQU
JURYATAUTIOPW            .LLL...LL.RRR            IOPW
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL

pattern = RRRR
THAETURQU                .LLL..RRR
JURYATAUTIOPW            .LLL...LL.RRR
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL

pattern = LL
THAETURQU                .LLL..RRR                HA,AE
JURYATAUTIOPW            .LLL...LL.RRR            UR,RY,UT
TURIWOWQNQQUTYRIOPWMNHF  L..L..LLLL.LL.R..L.LLLL  WQ,QN,NQ,UT,MN,NH,HF
[download]