There are products out there that claim to do this conversion for you, but you can do it for free by exporting the Access tables to CSV format and then using the SQLite shell
] to import them into tables on SQLite.
I would suggest creating the tables on SQLite first to ensure that dates are interpreted as dates, ints as ints etc rather than relying on the import to determine what the data types are.
Don't add any indexes to the tables until after you have imported them.
With either Access or SQLite choose appropriate indexes to search the database(s) faster.
It will take some time to export then load but it only needs to be done once.
Just went to the SQLite site to check on something and also found this link to their converter
]. It claims to read from Access also.