No, these spells cannot save you from death by massive damage.
From the PFSRD (emphasis mine):
Massive Damage (Optional Rule):
If you ever sustain a single attack that deals an amount of damage equal to half your total hit points (minimum 50 points of damage) or more and it doesn’t kill you outright, you must make a DC 15 Fortitude save. If this saving throw fails, you die regardless of your current hit points.
Note in particular the part about killing you regardless of your current hit points. You could be reactively healed to full by these effects and it wouldn't save you, because they're simply preventing the damage from killing you outright. You're not dying due to your hit points being too low, you're dying because you failed a saving throw against an instant death effect: you don't fall unconscious, drop to zero HP, or pass go & collect $200, you just die.
Here's the sequence of events: Bob, a fighter with a maximum of 125 hit points, currently has 70 hit points and is under the effects of Nine Lives. Bob is struck by a storm giant for 90 damage, reducing him to -20, which would normally kill him. Nine Lives heals Bob for 3d6 (let's say 12), bringing him to a safe-ish -8 hit points. But this doesn't save Bob from the massive damage rule! Bob took damage that was both >= 50hp and at least half his max hit points in a single blow, so the massive damage rule triggers. The massive damage rule does not check Bob's current hit point, it just directly forces Bob to make a fortitude saving throw. Alas, Bob rolls a 2, and fails his save. Thus, per the massive damage rule, Bob dies no matter how many hit points he has.
Consider a second example: Bob is instead at full hit points (125), and is struck by a storm giant for 90. Bob is not reduced to zero by this damage, only 35, and so Nine Lives and similar effects do not trigger. But the massive damage rule doesn't care how many hit points Bob has left; its trigger is the amount of damage that Bob took. Bob still has to make a fortitude saving throw, and he will still die if he fails it, despite having 35 hit points left.
The only things that will save you from death by massive damage are effects that prevent you from taking the damage in the first place or reduce it below the trigger threshold, or succeeding on your fortitude saving throw (never listen to anyone who tells you Constitution can be a dump stat).