I'd use a fixed size buffer @buf with $paddding * 2 + 1 elements and always look at the middle line ($viewline) of the buffer. @interesting is a list of thing you're interested in.

@lines contains the data. I've used a list of numbers, but it could be text.

my @lines = 1 .. 20;
my @interesting = ( 1, 3, 6, 10 , 20 );
my $padding = 2;

my $bufsize  = 2 * $padding + 1;
my $viewline = $padding;
my @buf = ('') x $bufsize;

while ( @buf > 0 ) {
    my $line = shift @lines; # get some data
    shift @buf;              # shorten buffer
    push @buf, $line         # add new line
        if $line;            # if there was one

    print "-->@buf\n" # if there's something to see && it's interestin
+g
        if $buf[$viewline] 
           && grep $buf[$viewline] eq $_, @interesting;
}
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Output:

-->  1 2 3
-->1 2 3 4 5
-->4 5 6 7 8
-->8 9 10 11 12
-->18 19 20
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update: added the output