You need to call LimeLM::SetAPIKey("your API key here") before you make any function calls from LimeLM.php.
The errors you're getting are a result of you not call SetAPIKet. That is, the "not a valid cURL handle resource" the error is talking about is created when you call SetAPIKey(). So if you never call that function, the cURL resource is never created, and thus an error.
Does that make sense?