I follow a different philosophy when it comes to the LJBF speech.
I think that if a girl LJBFs you, the best thing you can do (and the least needy) is to completely agree with it. Don't drag your feet, don't put on any fronts about going with other girls instead, just agree. Be like "I agree, we should just be friends".
When given the LJBF speech, the majority of guys
whine (NEEDY),
argue (NEEDY), or
turn it down ("No, I don't want you as a friend; I have enough friends" = NEEDINESS IN DENIAL = SUPER NEEDY). All these things are needy and will get you permanently shut out. Believe me, I know; I did this crap for years.
When you agree with the LJBF speech ("Let's just be friends. No, for real, let's just be friends"), it mentally fucks girls up. They have completely lost all power over you; you've flipped the script on them. When done properly (meaning with true belief), the LJBF speech becomes nothing more than LMR. Its basically like a freeze out.
This demonstrates attractiveness and value on so many levels. First off, it demonstrates complete non-neediness. You like her, but you are not attached to the outcome. It also demonstrates a mindset of abundance: you like her, but you aren't hurt, angry, or upset, because you know you can have other girls (but don't actually say it!). LESSON: Don't say what you can sub-communicate instead! Also, if you do this, you're probably going to start hanging out with her even more, because this is a massive comfort booster. Shes knows you are secure enough that she can hang out with you exclusively without worrying about drama or outcomes, right up until you close her anyway.
Look, if you're getting the LJBF speech, that means that at some point she probably liked you, and was or is still sending you IOIs. Just because she doesn't want to date RIGHT NOW doesn't mean she isn't still into you. Trust me, as long as you're still hanging out, you can continue to build attraction and comfort, which means you can still close.
I NEVER overcame the LJBF speech until I stared doing this. I actually stumbled on it by accident last summer. I don't usually get the LJBF speech anymore, but have gotten it twice in the last 6 months, and both times I overcame it and closed within a week.
Even in the unlikely event that this doesn't work out (you probably weren't going to get her anyway), god forbid you still have her as a friend! And not just any friend: a girl who likes you and will socially proof you to other girls. The other guy who whined, argued, or said "I don't want you as a friend" will get the negative SPAM instead.