All the info is stored either on the device itself or synced via Blockstack if you wish to do so. The project is also entirely open-source - https://github.com/lannister-capital
I understand your intention, but you have a bit of an uphill battle. Users have to trust you on many levels:
1) The app running on your phone is powered by the software on github.
2) This will not change.
The only way I would use an app like this would be if it were offered by a financial institution that holds my assets. If your app caused me to lose money, I would be SOL. If their's did, they would be required to answer for it.
Lannister only holds references of your holdings at the moment. It doesn't store your holdings/assets directly, so there's no chance to be stolen, since they're not there.
Lannister is not a bank account or crypto wallet, it's a portfolio management app only. We don't ask or store private keys or any personal banking information of any kind.
1) The app running on your phone is powered by the software on github.
2) This will not change.
The only way I would use an app like this would be if it were offered by a financial institution that holds my assets. If your app caused me to lose money, I would be SOL. If their's did, they would be required to answer for it.