You don't tell us which SSL library you are using, but did you make sure that it is threadsafe and compiled for threading ?

As LWP dynamically loads stuff, you could maybe test the following program to further narrow it down:

use strict;
use Net::SSLeay; # or whatever other SSL implementation you use
use threads;

my $t = threads->new(\&threadedRequestThread)
  or die "Can't create thread\n";

print "Joining thread\n";
my @ret = $t->join();
print "Thread returned (@ret)\n";
exit(0);

# Actual Thread function
sub threadedRequestThread {
    print "Inside threadedRequestThread\n";
    return "A list of words";
}
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or, failing that program, you might need to call some routines in Net::SSLeay to initialize it.