Ok, the following assumes that the file is already sorted by invoice number and then timestamp.

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

#our $Logfile = 'file.log';
#open my $fh, $Logfile or die "Can't open $Logfile: $!\n";

my $fh = \*DATA; # Testing purposes


# The first element of @records is the "current" line.
# The second element is the "next" line, if any.
my @records = get_next_record($fh);

do {
  # Read the next line
  push @records, get_next_record($fh);

  if(
    ($records[0]{name} eq 'Larry' or $records[0]{name} eq 'Robb')
      and not
    (
      # No more lines
      $#records
        and
      # Not the name
      ($records[1]{name} eq 'Larry' or $records[1]{name} eq 'Robb')
    )
  ) {
    print $records[0]{record};

    # Skip to the next set of records, and start over.
    # ('skip' is removed immediately and is only for place-holding.)
    @records = ('skip', find_next_record_set($fh, $records[0]{inv}));
  }

  # Remove the old "current" line, and make the next line current.
  shift @records;
} while @records;

exit;


sub parse_record {
  my $record = shift;
  my %data = ('record' => $record);
  @data{qw(inv name date time)} = split(/\s+/, $record);
  return \%data;
}

sub get_next_record {
  my $fh = shift;
  my $rec = <$fh>;
  return defined($rec) ? parse_record($rec) : ();
}

sub find_next_record_set {
  my $fh = shift;
  my $rs = shift;
  my $line;

  1 while(defined($line = <$fh>) and $line =~ /^\Q$rs/);

  return defined($line) ? parse_record($line) : ();
}

__DATA__
1056128833340 Robb 2003-06-20 665 **
1056128833340 t028348 2003-06-20 607
1055439973653 T012697 2003-07-22 962
1055439973653 t012697 2003-07-22 948
1055439973653 t806174 2003-07-15 792
1055439973653 T806174 2003-07-15 791
1055439973653 t021191 2003-07-08 786
1055439973653 Robb 2003-06-17 503
1055439973653 Larry 2003-06-16 815 **
1055439973653 t021191 2003-06-12 646
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