If you want to include and use sqlite3 in your c/c++ project, you only have to make sure the correct linker flag is set:
Right click your project in the project explorer > Properties > C/C++ Build > Settings > IoT Poky 32-Bit G++ Linker > Libraries > add... "sqlite3" > ok
The poky linux distro installed on the Intel edison comes with a couple of preinstalled c/c++ libraries that can be directly used and linked into your own project, sqlite3 is one of them. You only have to make sure the library is included in the link command (see steps above), so no need to install the library yourself. You can check the list of available libraries via `ls /usr/include` on your intel edison.
Side note: The above procedure works in the current Intel® System Studio IoT Edition | IoT | Intel® Software on all OS because this version uses a docker container (with the exact same yocto poky linux installed) to natively compile your project, as a consequence the docker container contains the same libraries and simply adding the appropriate linker flag is sufficient. However the above procedure might not work with the former (deprecated) Intel Dev kit which uses cross-compiling instead of a docker container (however I didn't verify this)