Bonus: How much would the increase in lunar mass increase average tides? & which factors would cause the Earth to become uninhabitable?
It'd have to be pretty big. And by 'big', I mean instead of the moon orbiting the earth, the earth would become a satellite of the Moon.
And the Moon would be around the size of Jupiter.
I'm taking a guess from the context that the mechanism of uninhabitability that you're thinking about is tidal forces ripping the earth apart, or at least causing sufficient levels of vulcanism to make the formation of life impossible.
Basically, you're thinking about Io.
Io orbits Jupiter only about 10% further out than the Moon orbits the Earth (420,000km vs 385,000km), and because of that it's the most tectonically active thing in the solar system. Certainly no life is likely to ever form there.
HOWEVER, Europa orbits Jupiter at around 660,000km and even though the amount of radiant energy available is miniscule at that distance from the Sun, there's still a lot of hope that life could naturally evolve there. The earth would be more tectonically active at that distance than it is now, but not catastrophically so.
At a more reasonable 1millionkm orbit (where Ganymede sits relative to Jupiter), things would be just fine.
In fact, if you had the Earth orbiting a Jupiter-like gas giant at the same distance from the sun we are currently, then it would be just about as habitable as it is now. You'd have a much more complicated seasonal variation of course because instead of just the axial tilt you'd also have to take into account the effects of passing in front of and behind the gas giant, but other than that, humans would be just fine.
We'd just have MUCH more spectacular sunsets and eclipses.
EDIT: I realized there's another important factor that I didn't address. The other issue to consider is atmosphere retention.
Jupiter's moons all have very thin atmospheres for the same reasons that Mars does. First, they're not massive enough for gravity to do all the work and Second, they don't generate enough of a magnetic field to prevent an atmosphere from being ionized and stripped away by solar wind or (in the case of Jupiter's moons), by the massive magnetosphere of Jupiter itself.
Now, this would be a problem for earth too if it had a really massive neighbor because now you've got the electromagnetic effects on the atmosphere to consider. Earth generates a MUCH stronger magnetic field of its own than any of Jupiter's satellites, which would mitigate the effects somewhat, but not entirely.
Here again proximity is the key factor. If Earth were orbiting Jupiter at the same distance as Io does, not only would you have the tidally created vulcanism to worry about, you'd also have massive magnetic storms. I'm not enough of a physicist to know exactly where the safe limit would be, but there's a range where Earth might be far enough away to avoid the catastrophic volcano problem, but still close enough that the magnetic storms would render the atmosphere unsuitable for life.
On the other hand, you also still have a nice sweet spot the Earth could sit in where its own magnetosphere is strong enough to protect the atmosphere, and everything is copacetic.
You'd probably have some pretty spectactular Aurora Borealis EVERYWHERE, EVERY NIGHT, but that's sort of a win/win in my book.