Is LiteOn A Good PSU Make?

No a budget Chinese brand.

NOOOOOOOOOOOOOOOOOOOO.
Name brand only.
You NEVER buy a PSU from a company you never heard that manufactures PSUs.

They actually make many PSU's for the OEM's. http://www.overclock.net/t/790535/lite-on-psu-is-actual...

If a PSU dies, can it take things like the HDD with it?

Yes

How long would it take for a LiteOn PSU to even die? Just because they aren't that good does that mean they will die faster? Also this is not my PC that has the PSU  .

It can take anywhere from days to many years. It is all a matter of load and environment even quality PSU's can fail but most quality PSU's have internal protection that protects other components.

It's in a 3 year old HP computer. Do you think it would need to be replaced with like a seasonic PSU?

I suspected so much any quality PSU can replace it this is a popular replacement http://www.newegg.com/Product/Product.aspx?Item=N82E168...

Hi - You have an hd7970, not a sound strategy to risk that level gpu
with a low end psu with Chinese caps, etc. You are playing with fire.

Your sys tdp with that gpu is approx 335w without oc, I suggest
a quality 550w (no harm in more) psu.

And yes, you were right on Seasonic or other quality brands.

Tom

Like I said, this is not my PC I'm talking about : ).

Right - shouldn't have said "You" in my reply.

Tom