Lightning Bolts do not appear if they are more than 64 blocks away from the player. This makes it so in order to see the actual lightning bolt you must be close to it. I have seen lightning bolts strike further away then this in previous versions with it still rendering.
UPDATE: In 15w35b (and possibly 15w35a, I haven't checked that version) the distance seems to have been increased to about 95 blocks.
Recreate this by using this command:
/summon LightningBolt ~65 ~ ~
and look in the positive X direction.
Or if you are running 15w35b or higher:
/summon LightningBolt ~96 ~ ~
The image below shows this working correctly in version 1.6.4
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Added an image of lightning rendering correctly in version 1.6.4

Can confirm. They used to render much mre further in previous versions.
Now you need to be really really close to see the lightning.
(btw the lightning bold rendering is also affected. It will render behind some objects like water)

Confirm.

Confirmed for 1.8 pre-release 3. Makes it a bit tougher to hunt for charged creepers if you can't see where lightning hit just 4 chunks away.

confirmed for 1.8.1 pre-5

Confirmed for 1.8.2 Pre-1

Glad I found this, I was wondering why I was not able to see the lightning bolts.
Version 1.8.1

Confirmed for 1.8.3.

Confirmed for 1.8.4.

Still in the game in 1.8.7.

In 15w35b the distance seems to have been increased to 95 blocks, it's possible this change happened before 15w35b, I haven't tested it in previous 1.9 snapshots.

This issue has been resolved as of 15w38a. You can now see any lightning bolt that is within your render distance. It should be marked as resolved.

I was wrong, the render distance for lightning seems to be based on your render distance setting.
However, the lightning's render distance is about half of your total render distance.
When I set my render distance to 32 chunks, the lightning render distance was 160 blocks.
The 96 block limit was found while my render distance was set to 12.

Is this still an issue in the most recent versions (currently that is 1.10.2, or 16w42a) of Minecraft? If so, please update the affected versions and help us keeping this ticket updated from time to time.

Can confirm this on both 1.10.2 and 16w42a. Wow, this bug was unnoticed for a while.

I just tested. This issue is not present in 1.10.2 or 16w42a. I can tell you, the render distance for lightning is dependent on the render distance of the player. In other words the bug is fixed and should be marked resolved.

For me lightning still dissapears few chunks away from it, that's on 12-16 chunks render distance. How is it fixed when it is present (at least for me)? It is not supposed to dissapear like that, there's no purpose for it.

Right now it is fixed as I said in my previous comment. I tested on plain vanilla 1.10 and 16w42a with no rendering issues. The reason you are only seeing lightning no more than 95 blocks away is because you are on render distance 12. At that render distance lightning will only render 95 blocks away at most. As you increase the render distance from 12 (95 block max) I observed that at 14 chunks the lightning will render out to 111 blocks and at 16 chunks renders up to 127 blocks away. This pattern continues up to a maximum of 159 blocks. This confirms this to be resolved as the view distance of lightning is based upon render distance.

It depends on render distance. But lightning bolt render distance is smaller than set in video settings.

Look at what Jeremy wrote in his last comment. It works exactly like that, and I did some extensive tests with it. Looks all good to me.