Do I need a tune for a cold air intake on an LS?

Not strictly — Summit treats an intake as a garage bolt-on that runs on the stock tune. It's still better tuned.

• Bolt-ons specifically: Summit's LS upgrade guides treat intake, exhaust and similar bolt-ons as garage jobs that run, but note the tune won't be optimized. Their advice is to follow them with a chassis-dyno session. On a stock LS6, Summit puts basic bolt-ons plus tuning at about 340 → 400 whp.
• The general rule: LSX Magazine's rule is that any change that significantly alters airflow or fuel flow (injectors, cam, throttle body) needs a custom calibration, because the stock fuel and timing data no longer match the engine.

If headers and exhaust are also planned, one tune after all of it covers the whole package.

Want to do it yourself? See who tunes it, and how to learn.