First of all, to answer your question directly, just have script1 check for the existence of a particular file; if that file doesn't exist, create it and run script2:

my $LOCKFILE = 'script1.lock';
if (!-e $LOCKFILE) {
   open FH, ">$LOCKFILE" or die $!;
   close FH;
   system("perl script2.pl");
}
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However, if they're both perl scripts, it seems silly to do a fork and invoke another perl interpreter to run it. Can't you just use or require it and call whatever function(s) you need directly?