OK took your code at face value and made some fundamental changes:

#!/usr/bin/perl

use strict;

while ($lines = <DATA>){
    $word = split "", $lines;
    
    print $word."\n";
}

print "\n\n";
exit 0;
__END__
tutor
teacher
tinker
sailor
[download]

and when I ran it got:

$ ./fix.pl 
Global symbol "$lines" requires explicit package name at ./fix.pl line
+ 5.
Global symbol "$word" requires explicit package name at ./fix.pl line 
+6.
Global symbol "$lines" requires explicit package name at ./fix.pl line
+ 6.
Global symbol "$word" requires explicit package name at ./fix.pl line 
+8.
Execution of ./fix.pl aborted due to compilation errors.
[download]

which is not too surprising. So the next set of changes:

#!/usr/bin/perl

use strict;

while (my $lines = <DATA>){
    my $word = split "", $lines;
    
    print $word."\n";
}

print "\n\n";
exit 0;
__END__
tutor
teacher
tinker
sailor
[download]

and now when we run it we get:

$ ./fix.pl 
6
8
7
8
[download]

pretty much as you describe. So let's make another change:

#!/usr/bin/perl

use strict;

while (my $lines = <DATA>){
    my ($word) = split "", $lines;
    
    print $word."\n";
}

print "\n\n";
exit 0;
__END__
tutor
teacher
tinker
sailor
[download]

which gives us:

$ ./fix.pl 
t
t
t
s
[download]

At this point I have a couple of comments to make:

1. Remember: the function split() returns an array based on the regex designating where to split the string. In this case you pass in an empty string which causes your $lines variable to be split on every character. (was that your intention?)
2. Without the enclosing parenthesis around $word you are using an array in a scalar context which means you are going to get the length of that array as a scalar not the value of the array itself.

Hope this helps you on your way....

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