You'll have to understand that an Arduino is not based on a microprocessor and is therefore unable to support the more than just one language as it lacks a software stack and its IDE is the only software it has. Now, this IDE just supports C/C++ syntax, libraries, and functions, which essentially means that your LWM2M Leshan Client written in Java will not work on the Anduino.
So, as an alternative, you could run a C/C++ based LWM2M client implementation like Eclipse Wakaama project on the Arduino instead of the Eclipse Leshan. Then again, without a software stack, porting even Wakaama to Arduino can be a task if you're not proficient or highly skilled. What you'll need for it are Arduino compatible libraries for CoAP and probably Arduino OTA. Otherwise, you could just switch to an Arduino Yun, which offers a Linux software stack, and you can easily port Wakaama to it.