Q:

Should I use "other" or "another" in the following case?

The dogs were put in pairs, one with a lever that stopped the shocks,
  and other/another with a lever that didn't.

Should I use other or another?

A:

Because you've already introduced the dogs earlier on in the sentence I'd go with:

The dogs were put in pairs, one with a lever that stopped the shocks, and the other with a lever that didn't.

Notice I can't say "... and other with...", I need to add the definite article.

A:

you can use both other and another.
other is used in a sentence before the plural or uncountable nouns.
     `eg: other people have problems too.`

but another is used in a sentence before the singular and countable nouns.
    `eg:  I would like another piece of cake`

here in this sentence use of another will be correct, because you are representing a single dog not group of dogs.

