It's a bit tricky to use SQLite in Lambda servers. However, @Kamyar Safari is not wrong and he is correct(almost) that the SQLite database is not permanent but it is not the only factor here. I recommend considering other alternatives like MySql/Postgres or ... that are available permanently on another server. Why you can not use it like this:
For number one 1 can't think anything except changing your configuration.
For the second solution, you to have a good knowledge of AWS. Use these docs for help
The last solution will not solve anything perfectly and It's just for you to experiment with the default configuration. Data still is inconsistent and if you decrease the reserved functions then you lose the data. And also more expensive because the lambda will not be destroyed(this feature is for high-traffic sites, not this issue)
https://docs.aws.amazon.com/lambda/latest/dg/configuration-concurrency.html