In order to stop the missile launch/ you must have saved ED-E from Ulysses' Temple. This makes it impossible to have both the Divide Survivor perk and the Lonesome Road perk at the same time.
It is the only guaranteed way to get an Idolized status with the Brotherhood of Steel when combined with the reputation gained during the quest Still in the Dark.
The SPECIAL point must be added. If you have them maxed out, then you will not be able to continue.
FIX: PC users can use the console command "cam" that will just close the menu and you'll be able to continue.
Another way to fix this is to type "player.forceav (put S.P.E.C.I.A.L skill here without parenthesis, example can be player.forceav charisma 9) 1-9" into the console before heading to the Canyon Wreckage at the end of the Lonesome Road.
FIX: If you have the DLC Old World Blues, you can transportalpond back to BigMT and then back with getting the perks. Can only be done if missile has been fired at someone, however, Dry Wells and The Long 15 will not be accessible.