John is eating little less salt than usual.

This one isn't correct; it would always be:

John is eating a little less salt than usual.

The description of the quantity should be able to stand on its own as a noun. So if someone asks:

How much salt is John eating, compared to his usual amount?

You would answer:

A little less.

And not:

Little less.

Similar phrases would be:

A great deal more.

A lot less.

However, "little" seems to be somewhat of a special case, in that we don't need to say anything like "a little amount", "a little" suffices of its own to describe the quantity.

John is eating little less salt than usual.

This one isn't correct for this context; it would always be:

John is eating a little less salt than usual.

The description of the quantity should be able to stand on its own as a noun. So if someone asks:

How much salt is John eating, compared to his usual amount?

You would answer:

A little less.

And not:

Little less.

Similar phrases would be:

A great deal more.

A lot less.

However, "little" seems to be somewhat of a special case, in that we don't need to say anything like "a little amount", "a little" suffices of its own to describe the quantity.

UPDATE

With regards to:

John is eating little less salt than usual.

This can actually be used, but means something different.

Consider the following statements:

There is a little snow on the ground.

There is little snow on the ground.

The difference has to do with expectation, with the first statement implying either neutrality (no expectation), or that we weren't expecting to see any snow, and the second statement implying that we were actually expecting to see more snow than there currently is.

So, going back to the initial example, if John had told us he was going to vastly reduce the amount of salt he eats, but had only reduced his intake by a small amount, the following would actually make sense.

How much salt has John been eating?

John is eating little less salt than usual.