As a 1password user, the one thing I prefer about that app vs Lastpass is the duration of Touch ID for the iOS app.
There should be a setting to retain Touch ID until the phone reboots. I find I'm entering my master password WAY too often on the Lastpass iOS app. I understand requiring the master password when the phone reboots (just like a secure iOS implementation requires the login password rather than touch ID after a reboot), but to ask me to type in my master password multiple times per day is a deal-breaker.
I have looked in the app settings extensively and haven't seen the setting to allow this behavior.
Check your Settings: Security: Auto Logout value. Something somewhere isn't set correctly as I use the iOS on multiple iPhones and iPads and very very rarely have to log in other than after a reboot. Just touch my finger or Face ID depending on which device. It works exactly as you describe wanting it to work.
Could you double check these settings in the LastPass app?
In the LastPass app, go to Settings > Security > adjust the Lock Options and Auto Logout settings (and make sure the Log Out on Close option is also turned off.) The Lock Options setting is how often you'd like to have the LastPass app require Face ID/PIN code/Touch ID verification, and the Auto Logout setting is how often the LastPass app will fully log out and require the master password to log in. For example, if you only want to have to use biometrics to unlock the LastPass app, you would set Auto Logout to Never and change the Lock Options to your desired time period--for example, you can set Lock Options to 24 hours to be prompted for biometric authentication every 24 hours.
If these settings are set correctly as explained above, we would recommend uninstalling the LastPass app, restarting your device, then reinstalling and re-enabling the above settings to your preference to see if that resolves this issue.