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.