For people who don't know, LastPass is, at its core, a service to store all your passwords that can be generated at random by LastPass, when people sign up. This creates a large, protected vault of log-in information. When a LastPass user encounters a log-in page, LastPass can automatically fill in the forms. The alternative would be to memorize your passwords, which, for the paranoid lot of us, are probably base-64, 32-character-long ones.
Let me give you an example of what happens when you use different forms. Etsy does both things which serves as a great example.
If I use their pop-up log-in button on the front page, this is what happens: http://i.imgur.com/x0rZZ.png. Note how none of the forms are filled out by LastPass.
If I use the "regular" HTML form on https://www.etsy.com/signin, this happens: http://i.imgur.com/9rtCp.png.
If the latter log-in is not available, I will have to click my LastPass icon, go to my vault, search for my Etsy credentials, copy them to my clipboard, and paste them into the pop-up form in order to log in.
But the worst is when the sign-up forms are pop-ups; now my credentials aren't saved, and you had better have a safe system for forgotten passwords, because you are bound to receive them. This is because the credentials aren't saved to LastPass, when they are in pop-up JavaScript. A royal pain in the ass.
I can only speak from personal experience, but for the love of everything UX, please, please, please use regular forms without any fancy JavaScript dingus, even though you just discovered jQuery for the first time.
With the increasing privacy concerns, LastPass users are going to grow in numbers - not dwindle - so you are going to annoy and possibly deter a lot of users inadvertently, if you don't get your log-in prompts right.