Another way, reading all lines into an array and chomping them then printing the join of the shifted first word and a slice of however many subsequent words are required.

$ perl -Mstrict -Mwarnings -E '
open my $inFH, q{<}, \ <<EOF or die $!;
The
quick
brown
fox
jumps
over
the
lazy
dog
EOF

chomp( my @words = <$inFH> );
close $inFH or die $!;

my $n = shift || 2;

say join q{ }, shift( @words ), @words[ 0 .. $n - 2 ]
   while scalar @words >= $n;'
The quick
quick brown
brown fox
fox jumps
jumps over
over the
the lazy
lazy dog
$
[download]

$ perl -Mstrict -Mwarnings -E '
open my $inFH, q{<}, \ <<EOF or die $!;
The
quick
brown
fox
jumps
over
the
lazy
dog
EOF

chomp( my @words = <$inFH> );
close $inFH or die $!;

my $n = shift || 2;

say join q{ }, shift( @words ), @words[ 0 .. $n - 2 ]
   while scalar @words >= $n;' 4
The quick brown fox
quick brown fox jumps
brown fox jumps over
fox jumps over the
jumps over the lazy
over the lazy dog
$
[download]

I hope this is of interest.