Compile the program with readline supoort. Readline is a common library that handles user input in interpreters such as bash and python. Fetch the source, the dependencies and configure with:
user@computer in: ~/src/sqlite-autoconf-3071602$ ./configure --enable-readline=yes
Consult the INSTALL file for details. Also, it's worth mentioning that there are probably binaries of sqlite3 with readline support already packaged for your distro. Look around.