Sending Message to a custom Pinpoint channel with Lambda

I'm trying to build an integration between Pinpoint and Lex for a two-way communication. I'm trying to build something similar to this solution on Amazon Blog but with minor modifications. Instead of sending the message via SMS channel, I need that message to be delivered to a Pinpoint Custom Channel. I'm unable to find any examples or API to send a direct message to a custom channel.

PS: I had to use Custom Channel due to the fact that, I wish to integrate Pinpoint with other channels like WhatsApp/ FB Messenger or internal endpoint.