Building Library Dependencies Separately

Hello,
If my lambda function has a c++ library dependency that I am building separately, and that will be dynamically loaded, what platform should I build the library dependency for? Linux ABI x86_64?
What happens with the GNU C Library ABI?
Will this be taken care of by the runtime as well?
I will be using the same platform to build those dependencies and to build the lambda function.

Thank you very much!