$i is not declared when your string is eval()d and you're not testing if the eval succeeds:

use strict;
use warnings;
#return a pointer to a function that should be invoked
sub makeLazy { 
   my ($inp) = @_;
      sub {
         eval $inp; 
         die if $@;
      };
}
my $i = 1;
my $part2 = makeLazy('print "\nnow its $i";');
print "\ni is ".$i++;
$part2->();
print "\ni is $i";
[download]

Global symbol "$i" requires explicit package name at (eval 1) line 1.
        ...propagated at test.pl line 8.
[download]

Why are you not just doing

use strict;
use warnings;
my $i = 1;
my $part2 = sub {print "\nnow its $i"; };
print "\ni is ".$i++;
$part2->();
print "\ni is $i";
[download]

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