Yes if you login to a site or app that isn’t already saved to your vault, you can save it from the mobile login screen to LastPass. First tap the password field and you should see the word “Passwords” come up over your keyboard. When you tap “Passwords” the LastPass screen will come up. Use your Touch ID or Face ID to authenticate and you’ll be in your vault.
Tap the + button at the top right corner. From there you can enter your username and passwords. Tap “Save”. Once you hit “Save”, you will be taken back to the login screen of the app or site and your credentials will be filled in for you.
You'll also want to be sure that LastPass is set as your Autofill service on iPhone as well by following these steps:
Exactly. This is so frustrating about LastPass. 1Password will automatically prompt to save the credentials of a new site you are logging into without you having to type it in again. LastPass will not do this and it made me switch back to 1Password. Saving passwords should be convenient not a hassle. Isn't that one of the points of a password manager? Ugh.