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