Thank you for all of your help raising this issue - our team has identified a fix for this issue and will include it in our next release which we plan to roll out within the next couple weeks.
Please keep an eye out for an update to the LastPass app in the App Store on your device, and install that update once it is available.
Could you try uninstalling the LastPass app, restarting your device, and then reinstalling the app to see if it resolves the issue?
Thanks for trying those steps out. To be sure that LastPass is set as your Autofill service, could you try going to your Settings app > Passwords > Autofill > Make sure Autofill is on and LastPass has a check mark and iCloud Keychain does not? Next, if you have multiple mobile web browser apps installed, you can go to Settings > Default Browser to select your preferred browser app to launch your Sites from your Vault within the LastPass for iOS app. By default, your Sites will launch using Safari.