Learn Italian: Spostandolo, il tecnico ha messo il riflettore sull'attrice. - Moving it, the technician put the spotlight on the actress.

With standalone gerunds (the -ando or -endo forms), object pronouns must be attached directly to the end to form a single word. While you would put the pronoun before a conjugated verb (like lo sposto), you can never say lo spostando.

What does the lo in spostandolo refer to, since the object hasn't been mentioned yet?

It refers forward to il riflettore (the spotlight) in the main clause. While English usually prefers to introduce the noun first ("Moving the spotlight, he put it..."), Italian often uses a pronoun in the introductory gerund phrase to refer to a noun that will appear later in the sentence.

Does adding the pronoun change which syllable gets stressed in spostandolo?

No, the stress stays on exactly the same vowel as it does in the base gerund (spostàndo). Even though the word is longer, you still stress that same syllable: spostàndolo.

If I wanted to say "Not moving it...", where would the negative word go?

You would place non right before the gerund phrase: Non spostandolo.... The pronoun lo remains firmly attached to the end of the verb.