I am building a python 3.6 AWS Lambda deploy package and was facing an issue with SQLite. 
In my code I am using nltk which has a import sqlite3 in one of the files.
Steps taken till now:

Deployment package has only python modules that I am using in the root. I get the error:
Unable to import module 'my_program': No module named '_sqlite3'
Added the _sqlite3.so from /home/my_username/anaconda2/envs/py3k/lib/python3.6/lib-dynload/_sqlite3.so into package root. Then my error changed to:
Unable to import module 'my_program': dynamic module does not define module export function (PyInit__sqlite3)
Added the SQLite precompiled binaries from sqlite.org to the root of my package but I still get the error as point #2.

My setup: Ubuntu 16.04, python3 virtual env
AWS lambda env: python3
How can I fix this problem?
This isn't a solution, but I have an explanation why.
Python 3 has support for sqlite in the standard library (stable to the point of pip knowing and not allowing installation of pysqlite). However, this library requires the sqlite developer tools (C libs) to be on the machine at runtime. Amazon's linux AMI does not have these installed by default, which is what AWS Lambda runs on (naked ami instances). I'm not sure if this means that sqlite support isn't installed or just won't work until the libraries are added, though, because I tested things in the wrong order.
Python 2 does not support sqlite in the standard library, you have to use a third party lib like pysqlite to get that support. This means that the binaries can be built more easily without depending on the machine state or path variables. 
My suggestion, which you've already done I see, is to just run that function in python 2.7 if you can (and make your unit testing just that much harder :/).
Because of the limitations (it being something baked into python's base libs in 3) it is more difficult to create a lambda-friendly deployment package. The only thing I can suggest is to either petition AWS to add that support to lambda or (if you can get away without actually using the sqlite pieces in nltk) copying anaconda by putting blank libraries that have the proper methods and attributes but don't actually do anything.
If you're curious about the latter, check out any of the fake/_sqlite3 files in an anaconda install. The idea is only to avoid import errors.
sqlite3 error on AWS lambda with Python 3