use Data::Dumper;

my $data = <<TXT;
T1 Line1
T2 Line2
   Line3
   Line4
T3 Line5
   Line6
ER
TXT

my(%h, $k);
for(split /\n/, $data) {
  last if /^ER\z/;
  /^(T\d+)/ and $k = $1;
  push @{ $h{$k} }, m< (?: T\d+ )? \s+ (.*) >x;
}

print Dumper(\%h);

__output__

$VAR1 = {
          'T1' => [
                    'Line1'
                  ],
          'T2' => [
                    'Line2',
                    'Line3',
                    'Line4'
                  ],
          'T3' => [
                    'Line5',
                    'Line6'
                  ]
        };