Do I need a tune after installing a supercharger on an LS?

Yes. What a boosted LS needs from the tune:

• Boost enrichment and timing: under boost the engine needs extra fuel and less timing. LSX Magazine's approach is to pull timing anywhere that may see boost, then add it back carefully on the dyno.
• Load sensing: a custom speed-density operating system with a matching MAP sensor (LSX Magazine cites up to 30 psi with a 3-bar setup). A mismatched MAP sensor badly corrupts fueling.
• Fuel system: Summit puts stock LS1 injectors at about 390 hp and the stock LS1 pump at about 450 hp, so most kits need fuel upgrades plus recalibration.

See fuel, E85 & boost.

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