There are quite a few ways to do this.
For example, you can write a small application (VB.Net, C#) which connects to the Access Database using OleDb and gets the data to a dataset. After that connect to the SQLite database using for example
System.Data.SQLite[
^] or OleDb again and insert the data from the dataset to the database.
A completely different approach could be to export the data from Access into a CSV file using
TransferText[
^] and then importing the data into SQLite using SQLite shell, see
sqlite - Importing Files[
^]