You are almost there, include the condition inside the split pattern:

use strict;

my $app_text = "one:partridge\ntwo:\nturtle doves\nthree:french hens\n
+";

foreach my $line (split /(?<!:)\n/, $app_text) {
  $line =~ s/\n//g;   # Eliminate internal "\n"s
  print "$line\n";

}
[download]

Outputs

one:partridge
two:turtle doves
three:french hens
[download]

Update: Corrected the split pattern to use lookbehinds, see perlre

citromatik