Is there some way to add a third party authorizer to (or by) a lightning network transaction?
I think you ask about escrow services in lightning. Generally there is a good opportunity to work with preimages. For example if we would move away from sha256 and would use ecdsa public private key encryption or a homomorphic hash function. Several parties could collaborative create a payment hash Wo sich they could only together generate the preimage. Stuff like this would also be possible with scriptless scripts. Also multiparty channels and channel factories could yield such functionality. So yes generally it is possible with lightning to go down this road but currently nothing of that is implemented to the protocol.