Darren is correct, there is no LiveCycle specific API's. I haven't dug into the Content Repository Client jar file to see what libraries it uses however I have monitored its communications to CRX and it is just performing HTTP POSTs and GETs.
So far, our requirements to interface with CRX have just been to access it to/from orchestrations (not Java directly). We've done that in three different ways:
1) Using the Content Repository Connector service
2) Using a custom component that performs standard HTTP POST/GET operations to POST or GET documents from CRX directly
3) Using a custom component that performs standard HTTP POST/GET operations to POST or GET to/from a Sling servlet with the Sling servlet performing the JCR work.
I'm not sure what client-side java libraries there may be for talking to CRX/Jackrabbit however I would expect that some exist.
Regards,
Rob