Transmit and Receive Continuously at the Same Time

I do not know, but I suspect that the document in this post might help.

And I suspect that the dualRXTX.cpp example code may help as well LimeSuite/src/examples at master · myriadrf/LimeSuite · GitHub

EDIT: I just re-read your question and now I think that you may be asking a fundamental programming question, which is not inherently related to SDR, “How do you use multithreading to have different things happening at the same time ?”
In C++ 11 you can use std::thread, or pthread’s is another option with any C/C++. Both have a high setup and tear down overheads, so you would typically setup threads and reuse them as much as possible. The performance of each should be the exact same since it is the OS that ultimately handles the creation of new threads.