Rewrite legacy php-native code to Laravel with no downtime

Question

I'm working in large app that have below module where every module have relation each other, the module is:

1. Fiance
2. Production
3. Plan
4. Laboratory

This app written in really-really php-native code with many security concern. I'm trying to rewrite it to Laravel Framework to make it better and easy to maintain.

My problem to rewrite this code is this app run on top of bad database design with this situation:

1. Many table is not normalized
2. Transaction table with master-detail record combined into one table. Example: Order transaction that should have two table orders and order_detail combined to one table named order_transaction

My task is to make sure user still can use the app while the development is start. So when the Finance module is already released, user will redirected to new app.

legacy app and new app should have single data source or synced data source

My question is: how to address this problem ?