Your

my @lines;

while (<DATA>)
{
   push @lines,$_;
}
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could more simply be written as

my @lines = <DATA>;
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Rather than reading the file into an array, sorting it using a routine then printing it out, you could sort and print directly using a GRT.

$ perl -Mstrict -Mwarnings -E '
open my $inFH, q{<}, \ <<EOD or die $!;
912828Q86       Note    1-Year  2016-05-25      2016-05-27      2018-0
+4-30      100.003850      NULL
912796HD4       Bill    4-Week  2016-01-26      2016-01-28      2016-0
+2-25      99.977056       NULL
912810RS9       Bond    30-Year 2016-05-12      2016-05-16      2046-0
+5-15      97.619462       2.500000
912810RQ3       Bond    29-Year 2016-04-14      2016-04-15      2046-0
+2-15      98.011430       2.500000
912796HD4       Bill    4-Week  2016-01-26      2016-01-28      2016-0
+2-25      99.977056       NULL
912828N71       Note    9-Year  2016-05-19      2016-05-31      2026-0
+1-15      103.533587      0.625000
EOD

print for
   map { unpack q{x4a*}, $_ }
   sort
   map { pack q{a4a*}, ( split )[ 1 ], $_ }
   <$inFH>;'
912796HD4       Bill    4-Week  2016-01-26      2016-01-28      2016-0
+2-25      99.977056       NULL
912796HD4       Bill    4-Week  2016-01-26      2016-01-28      2016-0
+2-25      99.977056       NULL
912810RQ3       Bond    29-Year 2016-04-14      2016-04-15      2046-0
+2-15      98.011430       2.500000
912810RS9       Bond    30-Year 2016-05-12      2016-05-16      2046-0
+5-15      97.619462       2.500000
912828N71       Note    9-Year  2016-05-19      2016-05-31      2026-0
+1-15      103.533587      0.625000
912828Q86       Note    1-Year  2016-05-25      2016-05-27      2018-0
+4-30      100.003850      NULL
$
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Note that this code is a little naive in that it relies on the words in the sorting column all being the same length. More robust would be to use unpack, or perhaps substr, rather than split to extract the entire column for sorting including any trailing spaces so that the code would cope if "Invoice" cropped up.

I hope this is of interest.