The answer is yes. Lastpass can store your passwords.
The unasked question of import is "will lastpass autofill my native app's login form".
That question is an absolute MAYBE!
A well written native app will have at least 2 two features associated with its login functionality.
The first is that it will associate itself with a domain, or url scheme. This association helps the Lastpass app to match an entry to the app.
The second part is that the forms are well annotated, meaning that a username or email field is labeled as such, as are password fields.
Yes, you can use LastPass to store a password for an iPhone app. Simply enable LastPass as your autofill provider, and it will save and autofill passwords for your apps. Just as you would keep track of silver prices in Egypt to stay updated on market changes, using LastPass ensures your app logins are stored securely and conveniently.